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On The Compactification Of Moduli Spaces For Algebraic K3 Surfaces
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Book Synopsis On the Compactification of Moduli Spaces for Algebraic $K3$ Surfaces by : Francesco Scattone
Download or read book On the Compactification of Moduli Spaces for Algebraic $K3$ Surfaces written by Francesco Scattone and published by American Mathematical Soc.. This book was released on 1987 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the problem of describing compact moduli spaces for algebraic [italic]K3 surfaces of given degree 2[italic]k.
Book Synopsis On the Compactification of Moduli Spaces for Algebraic K3 Surfaces by : Francesco Scattone
Download or read book On the Compactification of Moduli Spaces for Algebraic K3 Surfaces written by Francesco Scattone and published by . This book was released on 1985 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis K3 Projective Models in Scrolls by : Trygve Johnsen
Download or read book K3 Projective Models in Scrolls written by Trygve Johnsen and published by Springer Science & Business Media. This book was released on 2004 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts
Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Book Synopsis Compactifying Moduli Spaces by : Paul Hacking
Download or read book Compactifying Moduli Spaces written by Paul Hacking and published by Birkhäuser. This book was released on 2016-02-04 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.
Book Synopsis Singularities of Differentiable Maps by : V.I. Arnold
Download or read book Singularities of Differentiable Maps written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
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: Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.
Author :Sebastian Casalaina-Martin Publisher :American Mathematical Society ISBN 13 :1470460203 Total Pages :112 pages Book Rating :4.4/5 (74 download)
Book Synopsis Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models by : Sebastian Casalaina-Martin
Download or read book Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models written by Sebastian Casalaina-Martin and published by American Mathematical Society. This book was released on 2023-02-13 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Local and Global Methods in Algebraic Geometry by : Nero Budur
Download or read book Local and Global Methods in Algebraic Geometry written by Nero Budur and published by American Mathematical Soc.. This book was released on 2018-07-26 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12–15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.
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).
Book Synopsis Geometry of Algebraic Curves by : Enrico Arbarello
Download or read book Geometry of Algebraic Curves written by Enrico Arbarello and published by Springer Science & Business Media. This book was released on 2011-03-10 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.
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.
Book Synopsis Proceedings of the 1984 Vancouver Conference in Algebraic Geometry by : James B. Carrell
Download or read book Proceedings of the 1984 Vancouver Conference in Algebraic Geometry written by James B. Carrell and published by American Mathematical Soc.. This book was released on 1986 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers a cross-section of the developments in modern algebraic geometry. This work covers topics including algebraic groups and representation theory, enumerative geometry, Schubert varieties, rationality, compactifications and surfaces.
Book Synopsis An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces by : Martin Schlichenmaier
Download or read book An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces written by Martin Schlichenmaier and published by Springer Science & Business Media. This book was released on 2010-02-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.
Book Synopsis Contributions to Algebraic Geometry by : Piotr Pragacz
Download or read book Contributions to Algebraic Geometry written by Piotr Pragacz and published by European Mathematical Society. This book was released on 2012 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are the outcome of the Impanga Conference on Algebraic Geometry in 2010 at the Banach Center in Bedlewo. The following spectrum of topics is covered: K3 surfaces and Enriques surfaces Prym varieties and their moduli invariants of singularities in birational geometry differential forms on singular spaces Minimal Model Program linear systems toric varieties Seshadri and packing constants equivariant cohomology Thom polynomials arithmetic questions The main purpose of the volume is to give comprehensive introductions to the above topics, starting from an elementary level and ending with a discussion of current research. The first four topics are represented by the notes from the mini courses held during the conference. In the articles, the reader will find classical results and methods, as well as modern ones. This book is addressed to researchers and graduate students in algebraic geometry, singularity theory, and algebraic topology. Most of the material in this volume has not yet appeared in book form.
