Arc Schemes and Singularities

Arc Schemes and Singularities
Title Arc Schemes and Singularities PDF eBook
Author David Bourqui
Publisher Wspc (Europe)
Pages 0
Release 2020
Genre Algebraic spaces
ISBN 9781786347190

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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.

Arc Schemes And Singularities

Arc Schemes And Singularities
Title Arc Schemes And Singularities PDF eBook
Author David Bourqui
Publisher World Scientific
Pages 312
Release 2020-03-05
Genre Mathematics
ISBN 1786347210

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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.

Handbook of Geometry and Topology of Singularities IV

Handbook of Geometry and Topology of Singularities IV
Title Handbook of Geometry and Topology of Singularities IV PDF eBook
Author José Luis Cisneros-Molina
Publisher Springer Nature
Pages 622
Release 2023-11-10
Genre Mathematics
ISBN 3031319257

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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.

Algebraic Geometry: Salt Lake City 2015

Algebraic Geometry: Salt Lake City 2015
Title Algebraic Geometry: Salt Lake City 2015 PDF eBook
Author Tommaso de Fernex
Publisher American Mathematical Soc.
Pages 674
Release 2018-06-01
Genre Mathematics
ISBN 1470435772

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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.

Combinatorics and Physics

Combinatorics and Physics
Title Combinatorics and Physics PDF eBook
Author Kurusch Ebrahimi-Fard
Publisher American Mathematical Soc.
Pages 480
Release 2011
Genre Mathematics
ISBN 0821853295

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This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.

Representations and Nilpotent Orbits of Lie Algebraic Systems

Representations and Nilpotent Orbits of Lie Algebraic Systems
Title Representations and Nilpotent Orbits of Lie Algebraic Systems PDF eBook
Author Maria Gorelik
Publisher Springer Nature
Pages 563
Release 2019-10-18
Genre Mathematics
ISBN 3030235319

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This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Jet Schemes and Truncated Wedge Schemes

Jet Schemes and Truncated Wedge Schemes
Title Jet Schemes and Truncated Wedge Schemes PDF eBook
Author Cornelia Oichi Yuen
Publisher
Pages 208
Release 2006
Genre
ISBN

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