Syzygies in Hilbert schemes of complete intersections

Abstract

Let $e_1,...,e_c$ be positive integers and let $Y\subseteq {\mathbb{P}}^n$ be the monomial complete intersection defined by the vanishing of $x_1^{e_1},...,x_c^{e_c}$. In this paper we study sharp upper bounds on the number of equations and syzygies of subschemes parametrized by the Hilbert scheme of points $Hil{b}^d(Y)$, and discuss applications to the Hilbert scheme of points $Hil{b}^d(X)$ of arbitrary complete intersections $X\subseteq {\mathbb{P}}^n$.

Final version

References in corpus (2)

• On the Lex-plus-powers Conjecture
• On the growth of deviations

Cited by in corpus (2)

• Bounds for syzygies of monomial curves
• On minimal presentations of numerical monoids