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Author : Mircea Immanuel Mustaţǎ
Publisher : Unknown
Page : 130 pages
File Size : 42,5 Mb
Release : 2001
Category : Electronic
ISBN : UCAL:C3448304
Author : José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade
Publisher : Springer Nature
Page : 622 pages
File Size : 46,8 Mb
Release : 2023-11-10
Category : Mathematics
ISBN : 9783031319259
This 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.
Author : David Bourqui,Johannes Nicaise,Julien Sebag
Publisher : World Scientific
Page : 312 pages
File Size : 49,5 Mb
Release : 2020-03-05
Category : Mathematics
ISBN : 9781786347213
This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.
Author : Cornelia Oichi Yuen
Publisher : Unknown
Page : 208 pages
File Size : 52,9 Mb
Release : 2006
Category : Electronic
ISBN : UOM:39015064784658
Author : Shihoko Ishii
Publisher : Springer
Page : 236 pages
File Size : 40,6 Mb
Release : 2018-09-21
Category : Mathematics
ISBN : 9784431568377
This book is an introduction to singularities for graduate students and researchers. Algebraic geometry is said to have 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. First, mostly non-singular varieties were studied. 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. 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-dimensional 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. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.
Author : Dan Abramovich
Publisher : American Mathematical Soc.
Page : 539 pages
File Size : 52,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847039
Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.
Author : Alberto Corso,Juan Carlos Migliore,Claudia Polini
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 49,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840948
This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.
Author : Denis Chniot
Publisher : World Scientific
Page : 1083 pages
File Size : 50,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812704108
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,7 Mb
Release : 2024-07-04
Category : Electronic
ISBN : 9789814476393
Author : Raf Cluckers,Johannes Nicaise,Julien Sebag
Publisher : Cambridge University Press
Page : 347 pages
File Size : 49,6 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9781139499798
Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.
Author : Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag
Publisher : Springer
Page : 526 pages
File Size : 46,7 Mb
Release : 2018-09-15
Category : Mathematics
ISBN : 9781493978878
This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.
Author : Tommaso de Fernex,Brendan Hassett,Mircea Mustaţă,Martin Olsson,Mihnea Popa,Richard Thomas
Publisher : American Mathematical Soc.
Page : 655 pages
File Size : 40,9 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435776
This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.
Author : Antonio Campillo
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 53,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869000
Contains the proceedings of the Second International Workshop on Zeta Functions in Algebra and Geometry held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions.
Author : Nero Budur,Tommaso de Fernex,Roi Docampo,Kevin Tucker
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 40,8 Mb
Release : 2018-07-26
Category : Festschriften
ISBN : 9781470434885
This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12–15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.
Author : János Kollár
Publisher : Cambridge University Press
Page : 381 pages
File Size : 55,8 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9781107311473
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.