Author | : Jean-Paul Brasselet |
Publisher | : American Mathematical Soc. |
Total Pages | : 370 |
Release | : 2008 |
Genre | : Singularities (Mathematics) |
ISBN | : 082184458X |
Author | : Jean-Paul Brasselet |
Publisher | : American Mathematical Soc. |
Total Pages | : 370 |
Release | : 2008 |
Genre | : Singularities (Mathematics) |
ISBN | : 082184458X |
Author | : José Luis Cisneros Molina |
Publisher | : Springer Nature |
Total Pages | : 616 |
Release | : 2020-10-24 |
Genre | : Mathematics |
ISBN | : 3030530612 |
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.
Author | : Shihoko Ishii |
Publisher | : Springer |
Total Pages | : 227 |
Release | : 2014-11-19 |
Genre | : Mathematics |
ISBN | : 443155081X |
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.
Author | : Alexandru Dimca |
Publisher | : Springer Science & Business Media |
Total Pages | : 277 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461244048 |
Author | : Gert-Martin Greuel |
Publisher | : Springer Science & Business Media |
Total Pages | : 482 |
Release | : 2007-02-23 |
Genre | : Mathematics |
ISBN | : 3540284192 |
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.
Author | : Frédéric Pham |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2011-04-22 |
Genre | : Mathematics |
ISBN | : 0857296035 |
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
Author | : Christian de Duve |
Publisher | : Cambridge University Press |
Total Pages | : 288 |
Release | : 2005-10-24 |
Genre | : Mathematics |
ISBN | : 9780521841955 |
Publisher Description
Author | : János Kollár |
Publisher | : Cambridge University Press |
Total Pages | : 381 |
Release | : 2013-02-21 |
Genre | : Mathematics |
ISBN | : 1107035341 |
An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Author | : John Banville |
Publisher | : Swift Press |
Total Pages | : 331 |
Release | : 2023-07-21 |
Genre | : Fiction |
ISBN | : 1800753373 |
'This novel is essence of Banville ... a career summation' Daily Telegraph Felix Mordaunt, recently released from prison, steps from a flashy red sports car onto the estate of his youth. But there is a new family living in the drafty old house: descendants of the late, world-famous scientist Adam Godley. Felix must now vie with the idiosyncratic Godley family, with their harried housekeeper who becomes his landlady, with the recently commissioned biographer of Godley Sr., and with a wealthy and beautiful woman from his past who comes bearing an unusual request...