Splitting Deformations Of Degenerations Of Complex Curves
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Splitting Deformations Of Degenerations Of Complex Curves
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Author : Shigeru Takamura
language : en
Publisher: Springer
Release Date : 2006-10-11
Splitting Deformations Of Degenerations Of Complex Curves written by Shigeru Takamura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-11 with Mathematics categories.
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.
Splitting Deformations Of Degenerations Of Complex Curves
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Author : Shigeru Takamura
language : en
Publisher: Springer
Release Date : 2006-07-26
Splitting Deformations Of Degenerations Of Complex Curves written by Shigeru Takamura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-26 with Mathematics categories.
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.
Pseudo Periodic Maps And Degeneration Of Riemann Surfaces
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Author : Yukio Matsumoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-17
Pseudo Periodic Maps And Degeneration Of Riemann Surfaces written by Yukio Matsumoto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-17 with Mathematics categories.
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.
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
Journal Of The Mathematical Society Of Japan
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Author : Nihon Sūgakkai
language : en
Publisher:
Release Date : 2008
Journal Of The Mathematical Society Of Japan written by Nihon Sūgakkai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Hydrodynamic Limits Of The Boltzmann Equation
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Author : Laure Saint-Raymond
language : en
Publisher: Springer
Release Date : 2009-04-20
Hydrodynamic Limits Of The Boltzmann Equation written by Laure Saint-Raymond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Science categories.
The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics. Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.
The Dirac Spectrum
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Author : Nicolas Ginoux
language : en
Publisher: Springer
Release Date : 2009-05-30
The Dirac Spectrum written by Nicolas Ginoux and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-30 with Mathematics categories.
This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, it presents the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries.
Random Polymers
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Author : Frank den Hollander
language : en
Publisher: Springer
Release Date : 2009-04-09
Random Polymers written by Frank den Hollander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-09 with Mathematics categories.
Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.
Methods Of Contemporary Mathematical Statistical Physics
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Author : Marek Biskup
language : en
Publisher: Springer
Release Date : 2009-07-31
Methods Of Contemporary Mathematical Statistical Physics written by Marek Biskup and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-31 with Mathematics categories.
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.
Lectures On Topological Fluid Mechanics
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Author : Mitchell A. Berger
language : en
Publisher: Springer
Release Date : 2009-05-28
Lectures On Topological Fluid Mechanics written by Mitchell A. Berger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-28 with Science categories.
Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.