Modular Forms On The Moduli Space Of Polarised K3 Surfaces

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Lectures on K3 Surfaces

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1316797252
Total Pages : 499 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

K3 Surfaces and Their Moduli

Author : Carel Faber
Publisher : Birkhäuser
ISBN 13 : 331929959X
Total Pages : 403 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis K3 Surfaces and Their Moduli by : Carel Faber

Download or read book K3 Surfaces and Their Moduli written by Carel Faber and published by Birkhäuser. This book was released on 2016-04-22 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Author : Radu Laza
Publisher : Springer Science & Business Media
ISBN 13 : 146146403X
Total Pages : 613 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by : Radu Laza

Download or read book Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds written by Radu Laza and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Mordell–Weil Lattices

Author : Matthias Schütt
Publisher : Springer Nature
ISBN 13 : 9813293012
Total Pages : 436 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Mordell–Weil Lattices by : Matthias Schütt

Download or read book Mordell–Weil Lattices written by Matthias Schütt and published by Springer Nature. This book was released on 2019-10-17 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.

Modular And Automorphic Forms & Beyond

Author : Hossein Movasati
Publisher : World Scientific
ISBN 13 : 9811238693
Total Pages : 323 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Modular And Automorphic Forms & Beyond by : Hossein Movasati

Download or read book Modular And Automorphic Forms & Beyond written by Hossein Movasati and published by World Scientific. This book was released on 2021-10-12 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.

The Arithmetic and Geometry of Algebraic Cycles

Author : B. Brent Gordon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870204
Total Pages : 468 pages
Book Rating : 4.8/5 (72 download)

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Book Synopsis The Arithmetic and Geometry of Algebraic Cycles by : B. Brent Gordon

Download or read book The Arithmetic and Geometry of Algebraic Cycles written by B. Brent Gordon and published by American Mathematical Soc.. This book was released on 2000-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.

Topological Field Theory, Primitive Forms and Related Topics

Author : Masaki Kashiwara
Publisher : Springer Science & Business Media
ISBN 13 : 9780817639754
Total Pages : 512 pages
Book Rating : 4.6/5 (397 download)

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Book Synopsis Topological Field Theory, Primitive Forms and Related Topics by : Masaki Kashiwara

Download or read book Topological Field Theory, Primitive Forms and Related Topics written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 1998-12 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Author : Radu Laza
Publisher : Springer
ISBN 13 : 1493928309
Total Pages : 542 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Calabi-Yau Varieties: Arithmetic, Geometry and Physics by : Radu Laza

Download or read book Calabi-Yau Varieties: Arithmetic, Geometry and Physics written by Radu Laza and published by Springer. This book was released on 2015-08-27 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Topological Field Theory, Primitive Forms and Related Topics

Author : A. Kashiwara
Publisher : Springer Science & Business Media
ISBN 13 : 1461207053
Total Pages : 492 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Topological Field Theory, Primitive Forms and Related Topics by : A. Kashiwara

Download or read book Topological Field Theory, Primitive Forms and Related Topics written by A. Kashiwara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.

A Celebration of Algebraic Geometry

Author : Brendan Hassett
Publisher : American Mathematical Soc.
ISBN 13 : 0821889834
Total Pages : 614 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Celebration of Algebraic Geometry by : Brendan Hassett

Download or read book A Celebration of Algebraic Geometry written by Brendan Hassett and published by American Mathematical Soc.. This book was released on 2013-09-11 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Handbook of Moduli

Author : Gavril Farkas
Publisher :
ISBN 13 : 9781571462589
Total Pages : 594 pages
Book Rating : 4.4/5 (625 download)

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Book Synopsis Handbook of Moduli by : Gavril Farkas

Download or read book Handbook of Moduli written by Gavril Farkas and published by . This book was released on 2013 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Degeneration of Abelian Varieties

Author : Gerd Faltings
Publisher : Springer Science & Business Media
ISBN 13 : 3662026325
Total Pages : 328 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Degeneration of Abelian Varieties by : Gerd Faltings

Download or read book Degeneration of Abelian Varieties written by Gerd Faltings and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

Geometry of Moduli

Author : Jan Arthur Christophersen
Publisher : Springer
ISBN 13 : 3319948814
Total Pages : 330 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Geometry of Moduli by : Jan Arthur Christophersen

Download or read book Geometry of Moduli written by Jan Arthur Christophersen and published by Springer. This book was released on 2018-11-24 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

Moduli of Curves

Author : Joe Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387227377
Total Pages : 381 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Moduli of Curves by : Joe Harris

Download or read book Moduli of Curves written by Joe Harris and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.

Diophantine Geometry

Author : Marc Hindry
Publisher : Springer Science & Business Media
ISBN 13 : 1461212103
Total Pages : 574 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Diophantine Geometry by : Marc Hindry

Download or read book Diophantine Geometry written by Marc Hindry and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Number Theory

Author : Sinnou David
Publisher : Cambridge University Press
ISBN 13 : 0521559111
Total Pages : 305 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Number Theory by : Sinnou David

Download or read book Number Theory written by Sinnou David and published by Cambridge University Press. This book was released on 1995-05-18 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourteenth annual volume arising from the Seminaire de Theorie de Nombres de Paris covering the whole spectrum of number theory.

Classical Algebraic Geometry

Author : Igor V. Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 1139560786
Total Pages : 653 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Classical Algebraic Geometry by : Igor V. Dolgachev

Download or read book Classical Algebraic Geometry written by Igor V. Dolgachev and published by Cambridge University Press. This book was released on 2012-08-16 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.