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Cohomology of vector bundles and syzygies /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Cohomology of vector bundles and syzygies // Jerzy Weyman.
remainder title:	Cohomology of Vector Bundles & Syzygies
Author:	Weyman, Jerzy,
Description:	1 online resource (xiv, 371 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Syzygies (Mathematics) -
Online resource:	https://doi.org/10.1017/CBO9780511546556
ISBN:	9780511546556 (ebook)

Cohomology of vector bundles and syzygies /
Weyman, Jerzy,1955-

Cohomology of vector bundles and syzygies /Cohomology of Vector Bundles & SyzygiesJerzy Weyman. - 1 online resource (xiv, 371 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;149. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introductory Material --1.

The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

ISBN: 9780511546556 (ebook)Subjects--Topical Terms:

672046
Syzygies (Mathematics)

LC Class. No.: QA247 / .W49 2003

Dewey Class. No.: 512/.5

Cohomology of vector bundles and syzygies /
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100 1 $a Weyman, Jerzy, $d 1955- $e author. $3 1445541
245 1 0 $a Cohomology of vector bundles and syzygies / $c Jerzy Weyman.
246 3 $a Cohomology of Vector Bundles & Syzygies
264 1 $a Cambridge : $b Cambridge University Press, $c 2003.
300 $a 1 online resource (xiv, 371 pages) : $b digital, PDF file(s).
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338 $a online resource $b cr $2 rdacarrier
490 1 $a Cambridge tracts in mathematics ; $v 149
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $g 1. $t Introductory Material -- $g 2. $t Schur Functors and Schur Complexes -- $g 3. $t Grassmannians and Flag Varieties -- $g 4. $t Bott's Theorem -- $g 5. $t The Geometric Technique -- $g 6. $t The Determinantal Varieties -- $g 7. $t Higher Rank Varieties -- $g 8. $t The Nilpotent Orbit Closures -- $g 9. $t Resultants and Discriminants.
520 $a The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.
650 0 $a Syzygies (Mathematics) $3 672046
650 0 $a Vector bundles. $3 909677
650 0 $a Homology theory. $3 682984
776 0 8 $i Print version: $z 9780521621977
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511546556