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arXiv · 1903.08770

Syzygies in Hilbert schemes of complete intersections

Giulio Caviglia·Alessio Sammartano
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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 $Hilb^d(Y)$, and discuss applications to the Hilbert scheme of points $Hilb^d(X)$ of arbitrary complete intersections $X \subseteq \mathbb{P}^n$.

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BibTeXRIS

Giulio Caviglia, Alessio Sammartano. 2019-03-20. Syzygies in Hilbert schemes of complete intersections. https://doi.org/10.1016/j.jalgebra.2022.12.015

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