Schubert Varieties And Degeneracy Loci
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Schubert Varieties And Degeneracy Loci
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Author : William Fulton
language : en
Publisher: Springer
Release Date : 2006-11-13
Schubert Varieties And Degeneracy Loci written by William Fulton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-13 with Mathematics categories.
Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.
Schubert Varieties And Degeneracy Loci
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Author : William Fulton
language : en
Publisher:
Release Date : 2014-01-15
Schubert Varieties And Degeneracy Loci written by William Fulton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Symmetric Functions Schubert Polynomials And Degeneracy Loci
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Author : Laurent Manivel
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Symmetric Functions Schubert Polynomials And Degeneracy Loci written by Laurent Manivel 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 2001 with Computers categories.
This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetricfunctions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being ``semistandard''. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux andM.-P. Schutzenberger who deeply probed their combinatorial properties. It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidenceconditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notionsof topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.
Schubert Varieties Equivariant Cohomology And Characteristic Classes
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Author : Jarosław Buczyński
language : en
Publisher:
Release Date : 2018
Schubert Varieties Equivariant Cohomology And Characteristic Classes written by Jarosław Buczyński and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Algebraic topology categories.
IMPANGA stands for the activities of Algebraic Geometers at the Institute of Mathematics, Polish Academy of Sciences, including one of the most important seminars in algebraic geometry in Poland. The topics of the lectures usually fit within the framework of complex algebraic geometry and neighboring areas of mathematics. This volume is a collection of contributions by the participants of the conference IMPANGA15, organized by participants of the seminar, as well as notes from the major lecture series of the seminar in the period 2010-2015. Both original research papers and self-contained expository surveys can be found here. The articles circulate around a broad range of topics within algebraic geometry such as vector bundles, Schubert varieties, degeneracy loci, homogeneous spaces, equivariant cohomology, Thom polynomials, characteristic classes, symmetric functions and polynomials, and algebraic geometry in positive characteristic.
Equivariant Cohomology In Algebraic Geometry
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Author : David Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2023-11-30
Equivariant Cohomology In Algebraic Geometry written by David Anderson 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 2023-11-30 with Mathematics categories.
A graduate-level introduction to the core notions of equivariant cohomology, an indispensable tool in several areas of modern mathematics.
On Combinatorics Of Degeneracy Loci And H G B
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Author : Alexander T. F. Yong
language : en
Publisher:
Release Date : 2003
On Combinatorics Of Degeneracy Loci And H G B written by Alexander T. F. Yong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Topics In Cohomological Studies Of Algebraic Varieties
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Author : Piotr Pragacz
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Topics In Cohomological Studies Of Algebraic Varieties written by Piotr Pragacz 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 2006-03-30 with Mathematics categories.
The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis
Singular Loci Of Schubert Varieties
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Author : Sara Sarason
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Loci Of Schubert Varieties written by Sara Sarason 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 2012-12-06 with Mathematics categories.
"Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties – namely singular loci. The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan-Lusztig theory. New results are presented with sufficient examples to emphasize key points. A comprehensive bibliography, index, and tables – the latter not to be found elsewhere in the mathematics literature – round out this concise work. After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students.
Facets Of Algebraic Geometry
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Author : Paolo Aluffi
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-07
Facets Of Algebraic Geometry written by Paolo Aluffi 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 2022-04-07 with Mathematics categories.
Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
Standard Monomial Theory
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Author : V. Lakshmibai
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-23
Standard Monomial Theory written by V. Lakshmibai 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 2007-12-23 with Mathematics categories.
Schubert varieties provide an inductive tool for studying flag varieties. This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory on the one hand and standard monomial theory for Schubert varieties in certain special flag varieties on the other.