DMS Algebra Seminar

Speaker: Vaibhav Pandey (Purdue University)

Title: Symbolic powers of maximal minors under general linkage

Abstract: The symbolic powers of the minors of a generic matrix are well understood as determinantal rings are Algebras with Straightening Laws (ASLs). In particular, the ASL structure readily yields the fact that the symbolic powers of maximal minors agree with the ordinary powers. We prove that, quite surprisingly, the equality of the symbolic and ordinary powers holds for `the most general link' of maximal minors as well. Better still, the blowup algebras of the general link have precisely the same homological properties as those of the maximal minors. The key point is that these facts do not follow from standard techniques in liaison theory; we develop the novel tool of Gröbner degeneration of links in order to attack the problem. This is joint work with Matteo Varbaro.