000			02836 a2200265 4500
008			230127b |||||||| |||| 00| 0 eng d
020			_a9783031054792
082			_bBRU
100			_aBruns, Winfried
245			_aDeterminants, Grobner bases and cohomology
260			_bSpringer Nature, _c2022. _aSwitzerland:
300			_axiii, 507p.; _bhbk; _c24cm.
440			_aSpringer Monographs in Mathematics
504			_aInclude Index and Reference
520			_aThis 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. https://link.springer.com/book/10.1007/978-3-031-05480-8
650			_aDeterminantal varieties
650			_aSagbi bases
650			_aInitial algebras
650			_aCohomology of flag varieties
650			_aSchur functors
700			_aConca, Aldo _eCo- author
700			_aRaicu, Claudiu _eCo- author
700			_aVarbaro, Matteo _eCo- author
942			_2ddc _cTD
999			_c58535 _d58535