Beschreibung:
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.
Combines representation theoretic and geometric methods to study determinantal varieties
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.