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arXiv · 1208.1109

The Hilbert polynomial of a symbolic square

Kaloyan Slavov
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Abstract

Let $k$ be an algebraically closed field, and let $C\subset \mathbb{P}^n_k$ be a reduced closed subscheme with ideal sheaf $\mathcal{I}$. Let $\mathcal{I}^{<2>}$ be the second symbolic power of $\mathcal{I}$. When $C$ is an integral curve, we compute the Hilbert polynomial of $\mathcal{O}_{\mathbb{P}^n}/\mathcal{I}^{<2>}$ in terms of invariants of $C$.

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Kaloyan Slavov. 2012-08-06. The Hilbert polynomial of a symbolic square. https://doi.org/10.1080/00927872.2015.1023954

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