Syzygies in Hilbert schemes of complete intersections

Abstract

Let e1,…,ec be positive integers and let Y⊆Pn be the monomial complete intersection defined by the vanishing of x1e1,…,xcec. In this paper, we study sharp upper bounds on the number of equations and syzygies of subschemes parametrized by the Hilbert scheme of points Hilbd(Y), and discuss applications to the Hilbert scheme of points Hilbd(X) of arbitrary complete intersections X⊆Pn.