| Tag |
First Indicator |
Second Indicator |
Subfields |
| LEADER |
00000nam a22000005i 4500 |
| 001 |
in00004659821 |
| 006 |
m o d |
| 007 |
cr nn 008mamaa |
| 008 |
221202s2022 sz | o |||| 0|eng d |
| 005 |
20240805183649.1 |
| 020 |
|
|
|a 9783031054808
|z 9978-3-031-05480-8
|
| 024 |
7 |
|
|a 10.1007/978-3-031-05480-8
|2 doi
|
| 035 |
|
|
|a (DE-He213)978-3-031-05480-8
|
| 050 |
|
4 |
|a QA564-609
|
| 072 |
|
7 |
|a PBMW
|2 bicssc
|
| 072 |
|
7 |
|a MAT012010
|2 bisacsh
|
| 072 |
|
7 |
|a PBMW
|2 thema
|
| 082 |
0 |
4 |
|a 516.35
|2 23
|
| 100 |
1 |
|
|a Bruns, Winfried.
|e author.
|0 (orcid)0000-0002-7081-2261
|1 https://orcid.org/0000-0002-7081-2261
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
|
| 245 |
1 |
0 |
|a Determinants, Gröbner Bases and Cohomology /
|c by Winfried Bruns, Aldo Conca, Claudiu Raicu, Matteo Varbaro.
|
| 250 |
|
|
|a 1st ed. 2022.
|
| 264 |
|
1 |
|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2022.
|
| 300 |
|
|
|a 1 online resource (XIII, 507 pages 21 illustrations)
|
| 336 |
|
|
|a text
|b txt
|2 rdacontent
|
| 337 |
|
|
|a computer
|b c
|2 rdamedia
|
| 338 |
|
|
|a online resource
|b cr
|2 rdacarrier
|
| 347 |
|
|
|a text file
|b PDF
|2 rda
|
| 490 |
1 |
|
|a Springer Monographs in Mathematics,
|x 2196-9922
|
| 505 |
0 |
|
|a 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.
|
| 520 |
|
|
|a 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 interesting and important class of varieties.
|
| 650 |
|
0 |
|a Algebraic geometry.
|
| 650 |
|
0 |
|a Commutative algebra.
|
| 650 |
|
0 |
|a Commutative rings.
|
| 650 |
|
0 |
|a Algebra, Homological.
|
| 650 |
|
0 |
|a Discrete mathematics.
|
| 650 |
1 |
4 |
|a Algebraic Geometry.
|
| 650 |
2 |
4 |
|a Commutative Rings and Algebras.
|
| 650 |
2 |
4 |
|a Category Theory, Homological Algebra.
|
| 650 |
2 |
4 |
|a Discrete Mathematics.
|
| 655 |
|
7 |
|a Electronic books.
|2 local
|
| 700 |
1 |
|
|a Conca, Aldo.
|e author.
|0 (orcid)0000-0001-5897-9985
|1 https://orcid.org/0000-0001-5897-9985
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
|
| 700 |
1 |
|
|a Raicu, Claudiu.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
|
| 700 |
1 |
|
|a Varbaro, Matteo.
|e author.
|0 (orcid)0000-0003-2992-0401
|1 https://orcid.org/0000-0003-2992-0401
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
|
| 710 |
2 |
|
|a SpringerLink (Online service)
|
| 773 |
0 |
|
|t Springer Nature eBook
|
| 776 |
0 |
8 |
|i Printed edition:
|z 9783031054792
|
| 776 |
0 |
8 |
|i Printed edition:
|z 9783031054815
|
| 776 |
0 |
8 |
|i Printed edition:
|z 9783031054822
|
| 830 |
|
0 |
|a Springer Monographs in Mathematics,
|x 2196-9922
|
| 856 |
4 |
0 |
|u http://proxy.library.tamu.edu/login?url=https://doi.org/10.1007/978-3-031-05480-8
|z Connect to the full text of this electronic book
|t 0
|
| 950 |
|
|
|a Mathematics and Statistics (SpringerNature-11649)
|
| 950 |
|
|
|a Mathematics and Statistics (R0) (SpringerNature-43713)
|
| 955 |
|
|
|a Springer EBA Purchase
|
| 999 |
f |
f |
|s ea7a9dbb-33b0-4365-8ddd-849c7cabc807
|i d43a09cd-229a-4bb7-8cb6-c4894a45c482
|t 0
|
| 952 |
f |
f |
|a Texas A&M University
|b College Station
|c Electronic Resources
|d Available Online
|t 0
|e QA564-609
|h Library of Congress classification
|
| 998 |
f |
f |
|a QA564-609
|t 0
|l Available Online
|