Topology Of Algebraic Varieties And Singularities

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Topology Of Algebraic Varieties And Singularities

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Author : José Ignacio Cogolludo-Agustín
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Topology Of Algebraic Varieties And Singularities written by José Ignacio Cogolludo-Agustín and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honour of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain.

Topology Of Algebraic Varieties And Singularities

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Author : José Ignacio Cogolludo-Agustín
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-01-01

Topology Of Algebraic Varieties And Singularities written by José Ignacio Cogolludo-Agustín and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.

This volume contains four parts which look at algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements and singularities.

Handbook Of Geometry And Topology Of Singularities I

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Author : José Luis Cisneros Molina
language : en
Publisher: Springer Nature
Release Date : 2020-10-24

Handbook Of Geometry And Topology Of Singularities I written by José Luis Cisneros Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-24 with Mathematics categories.

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Introduction To Singularities And Deformations

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Author : Gert-Martin Greuel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-23

Introduction To Singularities And Deformations written by Gert-Martin Greuel 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 2007-02-23 with Mathematics categories.

Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Handbook Of Geometry And Topology Of Singularities Vii

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Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2025-03-01

Handbook Of Geometry And Topology Of Singularities Vii written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-01 with Mathematics categories.

This is the seventh volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of fourteen chapters that provide an in-depth and reader-friendly introduction to various important aspects of singularity theory. The volume begins with an outstanding exposition on Jim Damon’s contributions to singularity theory and its applications. Jim passed away in 2022 and he was one of the greatest mathematicians of recent times, having made remarkable contributions to singularity theory and its applications, mostly to medical image computing. The next chapter focuses on the singularities of real functions and their bifurcation sets. Then, we look at the perturbation theory of polynomials and linear operators, complex analytic frontal singularities, the global singularity theory of differentiable maps, and the singularities of holomorphic functions from a global point of view. The volume continues with an overview of new tools in singularity theory that spring from symplectic geometry and Floer-type homology theories. Then, it looks at the derivation of Lie algebras of isolated singularities and the three-dimensional rational isolated complete intersection singularities, as well as recent developments in algebraic K-stability and the stable degeneration conjecture. This volume also contains an interesting survey on V-filtrations, a theory began by Malgrange and Kashiwara that can be used to study nearby and vanishing cycle functors and introduced by Deligne. Then, we present a panoramic view of the Hodge, toric, and motivic methods in the study of Milnor fibers in singularity theory, both from local and global points of view. The Monodromy conjecture is also explained; this is a longstanding open problem in singularity theory that lies at the crossroads of number theory, algebra, analysis, geometry, and topology. This volume closes with recent developments in the study of the algebraic complexity of optimization problems in applied algebraic geometry and algebraic statistics. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Theory Of Singularities And Its Applications

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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Theory Of Singularities And Its Applications written by Vladimir Igorevich Arnolʹd and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

Covers such topics as construction of new knot invariants, stable cohomology of complementary spaces to diffusion diagrams, topological properties of spaces of Legendre maps, application of Weierstrass bifurcation points in projective curve flattenings, classification of singularities of projective surfaces with boundary, and control theory.

Introduction To Toric Varieties

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Author : William Fulton
language : en
Publisher: Princeton University Press
Release Date : 1993

Introduction To Toric Varieties written by William Fulton and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.

Sheaves In Topology

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Author : Alexandru Dimca
language : en
Publisher:
Release Date : 2011-03-30

Sheaves In Topology written by Alexandru Dimca and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.

Birational Geometry Of Algebraic Varieties

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Author : Janos Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2008-02-04

Birational Geometry Of Algebraic Varieties written by Janos Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-04 with Mathematics categories.

One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.

Singularities In Geometry And Topology Proceedings Of The Trieste Singularity Summer School And Workshop

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Author : Jean-paul Brasselet
language : en
Publisher: World Scientific
Release Date : 2007-01-16

Singularities In Geometry And Topology Proceedings Of The Trieste Singularity Summer School And Workshop written by Jean-paul Brasselet and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-16 with Mathematics categories.

Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.