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Splitting Deformations Of Degenerations Of Complex Curves
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Book Synopsis Splitting Deformations of Degenerations of Complex Curves by : Shigeru Takamura
Download or read book Splitting Deformations of Degenerations of Complex Curves written by Shigeru Takamura and published by Springer. This book was released on 2006-10-11 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a deformation theory for degenerations of complex curves; specifically, discussing deformations which induce splitting of the singular fiber of a degeneration. The author constructs a deformation of the degeneration in such a way that a subdivisor is "barked," or peeled off from the singular fiber. "Barking deformations" are related to deformations of surface singularities, in particular, cyclic quotient singularities, as well as the mapping class groups of Riemann surfaces via monodromies.
Book Synopsis Splitting Deformations of Degenerations of Complex Curves by : Shigeru Takamura
Download or read book Splitting Deformations of Degenerations of Complex Curves written by Shigeru Takamura and published by Springer Science & Business Media. This book was released on 2006-07-26 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a deformation theory for degenerations of complex curves; specifically, he treats deformations which induce splittings of the singular fiber of a degeneration. He constructs a deformation of the degeneration in such a way that a subdivisor is "barked" (peeled) off from the singular fiber. These "barking deformations" are related to deformations of surface singularities (in particular, cyclic quotient singularities) as well as the mapping class groups of Riemann surfaces (complex curves) via monodromies. Important applications, such as the classification of atomic degenerations, are also explained.
Book Synopsis Splitting Deformations of Degenerations of Complex Curves by : Shigeru Takamura
Download or read book Splitting Deformations of Degenerations of Complex Curves written by Shigeru Takamura and published by Springer. This book was released on 2006-07-26 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a deformation theory for degenerations of complex curves; specifically, discussing deformations which induce splitting of the singular fiber of a degeneration. The author constructs a deformation of the degeneration in such a way that a subdivisor is "barked," or peeled off from the singular fiber. "Barking deformations" are related to deformations of surface singularities, in particular, cyclic quotient singularities, as well as the mapping class groups of Riemann surfaces via monodromies.
Book Synopsis Towards the Classification of Atoms of Degenerations by : Shigeru Takamura
Download or read book Towards the Classification of Atoms of Degenerations written by Shigeru Takamura and published by . This book was released on 2001 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This is the second part of our series of works which make a systematic study of degenerations of complex curves, and their splitting deformations. In the present volume we discuss the construction of degenerations. Namely, we (1) reconstruct Matsumoto-Montesinos theory from algebro-geometric viewpoint, and (2) establish the connection between (cyclic and dihedral) quotient singularities and monodromies, and (3) show that among any topologically equivalent class of degenerations, there exists a linear degeneration (linear approximation theorem of degenerations). As a consequence, we recover a fundamental theorem due to Matsumoto and Montesinos."
Book Synopsis Towards the Classification of Atoms of Degenerations by : Shigeru Takamura
Download or read book Towards the Classification of Atoms of Degenerations written by Shigeru Takamura and published by . This book was released on 2001 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Motivated by the classification problem of atomic degenerations, in our series of papers, we make a systematic study for splitting deformations of degenerations of complex curves. We provide various new methods to construct splitting deformations, and deduce many splitting criteria of degenerations, which will be applied to the classification of atomic degenerations. Roughly, our criteria are separated into two types; in the first type the criteria are expressed in terms of the configuration of a singular fiber, and in the second type, in terms of sub-divisors of a singular fiber. In both types, our constructions are 'visible', in that we can view how the singular fiber is deformed. In the present paper, we demonstrate splitting criteria of the first type."
Book Synopsis Pseudo-periodic Maps and Degeneration of Riemann Surfaces by : Yukio Matsumoto
Download or read book Pseudo-periodic Maps and Degeneration of Riemann Surfaces written by Yukio Matsumoto and published by Springer Science & Business Media. This book was released on 2011-08-17 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.
Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos
Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
Book Synopsis Journal of the Mathematical Society of Japan by : Nihon Sūgakkai
Download or read book Journal of the Mathematical Society of Japan written by Nihon Sūgakkai and published by . This book was released on 2008 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Methods of Contemporary Mathematical Statistical Physics by : Marek Biskup
Download or read book Methods of Contemporary Mathematical Statistical Physics written by Marek Biskup and published by Springer. This book was released on 2009-07-31 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. It presents new results on phase transitions for gradient lattice models.
Book Synopsis Generalized Bessel Functions of the First Kind by : Árpád Baricz
Download or read book Generalized Bessel Functions of the First Kind written by Árpád Baricz and published by Springer Science & Business Media. This book was released on 2010-05-25 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions.
Book Synopsis Topological Complexity of Smooth Random Functions by : Robert Adler
Download or read book Topological Complexity of Smooth Random Functions written by Robert Adler and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
Book Synopsis Enumerative Invariants in Algebraic Geometry and String Theory by : Marcos Marino
Download or read book Enumerative Invariants in Algebraic Geometry and String Theory written by Marcos Marino and published by Springer Science & Business Media. This book was released on 2008-08-22 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Book Synopsis Stability of Queueing Networks by : Maury Bramson
Download or read book Stability of Queueing Networks written by Maury Bramson and published by Springer Science & Business Media. This book was released on 2008-06-26 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early 1990s, substantial attention has been devoted to the question of when such networks are stable. This volume presents a summary of such work. Emphasis is placed on the use of fluid models in showing stability, and on examples of queueing networks that are unstable even when the arrival rate is less than the service rate. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Alice Guionnet and Steffen Lauritzen.
Book Synopsis Some Mathematical Models from Population Genetics by : Alison Etheridge
Download or read book Some Mathematical Models from Population Genetics written by Alison Etheridge and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.
Book Synopsis Morrey and Campanato Meet Besov, Lizorkin and Triebel by : Wen Yuan
Download or read book Morrey and Campanato Meet Besov, Lizorkin and Triebel written by Wen Yuan and published by Springer Science & Business Media. This book was released on 2010-09-18 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.
Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm
Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer Science & Business Media. This book was released on 2010-09-03 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt:
