Alexandra Pevzner

Northeastern University

The transfer map and polynomials with common roots

Given an action of a finite group on a polynomial ring, the transfer map can be used to construct invariant polynomials. When the group action is modular, the image of the transfer is a proper ideal of the ring of invariants which has received extensive study. Still, explicit descriptions of the ideal and its relations remain elusive. In the case of the symmetric group over a field of positive characteristic, we show that the image of the transfer is an elimination ideal for a collection of polynomials with generic coefficients. From this description, we deduce a certain stability in the syzygies of this ideal as the number of variables in the polynomial ring grows. In certain cases, we give a determinantal description of the ideal and exhibit a linear minimal free resolution. Based on joint work with Harm Derksen.