MARC details
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| fixed length control field |
02836 a2200265 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
230127b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783031054792 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Item number |
BRU |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Bruns, Winfried |
| 245 ## - TITLE STATEMENT |
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| Title |
Determinants, Grobner bases and cohomology |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Springer Nature, |
| Date of publication, distribution, etc |
2022. |
| Place of publication, distribution, etc |
Switzerland: |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xiii, 507p.; |
| Other physical details |
hbk; |
| Dimensions |
24cm. |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE |
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| Title |
Springer Monographs in Mathematics |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Include Index and Reference |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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.<br/><br/>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.<br/><br/><br/><br/>https://link.springer.com/book/10.1007/978-3-031-05480-8 |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Determinantal varieties |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Sagbi bases |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Initial algebras |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Cohomology of flag varieties |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Schur functors |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Conca, Aldo |
| Relator term |
Co- author |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Raicu, Claudiu |
| Relator term |
Co- author |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Varbaro, Matteo |
| Relator term |
Co- author |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Item type |
Books |
