Title:  Annihilators of Homogeneous Symmetric Polynomials Under the Action of Partial Differentiation

 

Abstract:  Let E ans S be polynomial rings of degree n over a field k and let S act on E by partial differentiation.  Given a homogeneous symmetric polynomial f, what can we say about Ann(f)?  For a general polynomial the annihilator turns out to be as 'small' as possible.  We will discuss what 'small' means in this context and exhibit a specific polynomial that satisfies these conditions (based on work of M. Boij, J. Migliore, R. Miro-Roig, U. Nagel).