Singularities and Topology of Hypersurfaces
Author: Alexandru Dimca
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 277
ISBN-13: 1461244048
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Le Cycles and Hypersurface Singularities
Author: David Massey
Publisher: Springer
Published: 2006-11-14
Total Pages: 141
ISBN-13: 3540455213
DOWNLOAD EBOOKThis book describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Lê cycles of the hypersurface. The Lê cycles and their multiplicities - the Lê numbers - provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitrary dimension. The Lê numbers control many topological and geometric properties of such non-isolated hypersurface singularities. This book is intended for graduate students and researchers interested in complex analytic singularities.
Singular Points of Complex Hypersurfaces. (AM-61), Volume 61
Author: John Milnor
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 130
ISBN-13: 1400881811
DOWNLOAD EBOOKThe description for this book, Singular Points of Complex Hypersurfaces. (AM-61), Volume 61, will be forthcoming.
Introduction to Singularities and Deformations
Author: Gert-Martin Greuel
Publisher: Springer Science & Business Media
Published: 2007-02-23
Total Pages: 482
ISBN-13: 3540284192
DOWNLOAD EBOOKSingularity 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 II
Author: José Luis Cisneros-Molina
Publisher: Springer Nature
Published: 2021-11-01
Total Pages: 581
ISBN-13: 3030780244
DOWNLOAD EBOOKThis is the second volume of the Handbook of the Geometry and Topology of Singularities, 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. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. 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, and in other subjects. 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. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Singularities of the Minimal Model Program
Author: János Kollár
Publisher: Cambridge University Press
Published: 2013-02-21
Total Pages: 381
ISBN-13: 1107035341
DOWNLOAD EBOOKAn authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Intersection Homology & Perverse Sheaves
Author: Laurenţiu G. Maxim
Publisher: Springer Nature
Published: 2019-11-30
Total Pages: 278
ISBN-13: 3030276449
DOWNLOAD EBOOKThis textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.
Mixed Hodge Structures and Singularities
Author: Valentine S. Kulikov
Publisher: Cambridge University Press
Published: 1998-04-27
Total Pages: 210
ISBN-13: 9780521620604
DOWNLOAD EBOOKThis vital work is both an introduction to, and a survey of singularity theory, in particular, studying singularities by means of differential forms. Here, some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss-Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This is an excellent resource for all researchers in singularity theory, algebraic or differential geometry.
Handbook of Geometry and Topology of Singularities IV
Author: José Luis Cisneros-Molina
Publisher: Springer Nature
Published: 2023-11-10
Total Pages: 622
ISBN-13: 3031319257
DOWNLOAD EBOOKThis is the fourth 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 twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. 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. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
An Introduction to Contact Topology
Author: Hansjörg Geiges
Publisher: Cambridge University Press
Published: 2008-03-13
Total Pages: 8
ISBN-13: 1139467956
DOWNLOAD EBOOKThis text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
