Commutative Algebra and Algebraic Geometry: Symbolic Powers of Determinantal Ideals

Seminar | September 26 | 5-6 p.m. | 939 Evans Hall

 Leon Zhang, UC Berkeley

 Department of Mathematics

We give a description of certain products of minors of a generic matrix as pairs of standard Young tableaux. Under this description, the pairs of standard Young tableaux form a free basis of the polynomial ring whose variables are generic entries of that matrix. We also characterize the nth symbolic power of a determinantal ideal in terms of these pairs of standard Young tableaux, and use this to produce the irredundant primary decomposition of powers of determinantal ideals.