Schubert Varieties And Degeneracy Loci

Author : William Fulton
Publisher : Springer
ISBN 13 : 3540698043
Total Pages : 158 pages
Book Rating : 4.43/5 ( download)

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Download or read book Schubert Varieties and Degeneracy Loci written by William Fulton and published by Springer. This book was released on 2006-11-13 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : William Fulton
Publisher :
ISBN 13 : 9783662188125
Total Pages : 160 pages
Book Rating : 4.20/5 ( download)

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Download or read book Schubert Varieties and Degeneracy Loci written by William Fulton and published by . This book was released on 2014-01-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Laurent Manivel
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821541
Total Pages : 180 pages
Book Rating : 4.47/5 ( download)

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Download or read book Symmetric Functions, Schubert Polynomials and Degeneracy Loci written by Laurent Manivel and published by American Mathematical Soc.. This book was released on 2001 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David Anderson
Publisher : Cambridge University Press
ISBN 13 : 1009349988
Total Pages : 463 pages
Book Rating : 4.87/5 ( download)

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Download or read book Equivariant Cohomology in Algebraic Geometry written by David Anderson and published by Cambridge University Press. This book was released on 2023-11-30 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to the core notions of equivariant cohomology, an indispensable tool in several areas of modern mathematics.

Author : W. Fulton
Publisher : Springer Science & Business Media
ISBN 13 : 3662024217
Total Pages : 483 pages
Book Rating : 4.18/5 ( download)

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Download or read book Intersection Theory written by W. Fulton and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.

Author : Jarosław Buczyński
Publisher :
ISBN 13 : 9783037196823
Total Pages : 354 pages
Book Rating : 4.23/5 ( download)

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Download or read book Schubert Varieties, Equivariant Cohomology and Characteristic Classes written by Jarosław Buczyński and published by . This book was released on 2018 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
ISBN 13 : 3764373423
Total Pages : 321 pages
Book Rating : 4.29/5 ( download)

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Download or read book Topics in Cohomological Studies of Algebraic Varieties written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Sara Sarason
Publisher : Springer Science & Business Media
ISBN 13 : 146121324X
Total Pages : 254 pages
Book Rating : 4.46/5 ( download)

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Download or read book Singular Loci of Schubert Varieties written by Sara Sarason and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Author : Paolo Aluffi
Publisher : Cambridge University Press
ISBN 13 : 1108792510
Total Pages : 395 pages
Book Rating : 4.16/5 ( download)

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Download or read book Facets of Algebraic Geometry written by Paolo Aluffi and published by Cambridge University Press. This book was released on 2022-04-07 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.

Author : V. Lakshmibai
Publisher : Springer Science & Business Media
ISBN 13 : 3540767576
Total Pages : 271 pages
Book Rating : 4.72/5 ( download)

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Download or read book Standard Monomial Theory written by V. Lakshmibai and published by Springer Science & Business Media. This book was released on 2007-12-23 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.