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Determinants, Gröbner Bases and Cohomology, Hardcover by Bruns, Winfried; Con...
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Item specifics
- Condition
- Book Title
- Determinants, Gröbner Bases and Cohomology
- ISBN
- 9783031054792
- Subject Area
- Mathematics
- Publication Name
- Determinants, Gröbner Bases and Cohomology
- Item Length
- 9.3 in
- Publisher
- Springer International Publishing A&G
- Subject
- Algebra / Abstract, Geometry / Algebraic, Discrete Mathematics
- Publication Year
- 2022
- Series
- Springer Monographs in Mathematics Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Width
- 6.1 in
- Item Weight
- 33.3 Oz
- Number of Pages
- Xiii, 507 Pages
About this product
Product Information
This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra, representation theory and geometry. After a concise introduction to Gröbner and Sagbi bases, determinantal ideals are studied via the standard monomial theory and the straightening law. This opens the door for representation theoretic methods, such as the Robinson-Schensted-Knuth correspondence, which provide a description of the Gröbner bases of determinantal ideals, yielding homological and enumerative theorems on determinantal rings. Sagbi bases then lead to the introduction of toric methods. In positive characteristic, the Frobenius functor is used to study properties of singularities, such as F-regularity and F-rationality. Castelnuovo-Mumford regularity, an important complexity measure in commutative algebra and algebraic geometry, is introduced in the general setting of a Noetherian base ring and then applied to powers and products of ideals. The remainder of the book focuses on algebraic geometry, where general vanishing results for the cohomology of line bundles on flag varieties are presented and used to obtain asymptotic values of the regularity of symbolic powers of determinantal ideals. In characteristic zero, the Borel-Weil-Bott theorem provides sharper results for GL-invariant ideals. The book concludes with a computation of cohomology with support in determinantal ideals and a survey of their free resolutions. Determinants, Gröbner Bases and Cohomology provides a unique reference for the theory of determinantal ideals and varieties, as well as an introduction to the beautiful mathematics developed in their study. Accessible to graduate students with basic grounding in commutative algebra and algebraic geometry, it can be used alongside general texts to illustrate the theory with a particularly interestingand important class of varieties.
Product Identifiers
Publisher
Springer International Publishing A&G
ISBN-10
3031054792
ISBN-13
9783031054792
eBay Product ID (ePID)
26057265375
Product Key Features
Publication Name
Determinants, Gröbner Bases and Cohomology
Format
Hardcover
Language
English
Subject
Algebra / Abstract, Geometry / Algebraic, Discrete Mathematics
Publication Year
2022
Series
Springer Monographs in Mathematics Ser.
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xiii, 507 Pages
Dimensions
Item Length
9.3 in
Item Width
6.1 in
Item Weight
33.3 Oz
Additional Product Features
Number of Volumes
1 Vol.
Lc Classification Number
Qa564-609
Table of Content
1 Gröbner bases, initial ideals and initial algebras.- 2 More on Gröbner deformations.- 3 Determinantal ideals and the straightening law.- 4 Gröbner bases of determinantal ideals.- 5 Universal Gröbner bases.- 6 Algebras defined by minors.- 7 F-singularities of determinantal rings.- 8 Castelnuovo-Mumford regularity.- 9 Grassmannians, flag varieties, Schur functors and cohomology.- 10 Asymptotic regularity for symbolic powers of determinantal ideals.- 11 Cohomology and regularity in characteristic zero.
Copyright Date
2022
Illustrated
Yes
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