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Cohomology of vector bundles and syzygies /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Cohomology of vector bundles and syzygies // Jerzy Weyman.
其他題名:	Cohomology of Vector Bundles & Syzygies
作者:	Weyman, Jerzy,
面頁冊數:	1 online resource (xiv, 371 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Homology theory. -
電子資源:	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:

682984
Homology theory.

LC Class. No.: QA247 / .W49 2003

Dewey Class. No.: 512/.5

Cohomology of vector bundles and syzygies /
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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 Homology theory. $3 682984
650 0 $a Vector bundles. $3 909677
650 0 $a Syzygies (Mathematics) $3 672046
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