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arXiv · 1907.04290

Fundamental Group Schemes of Hilbert Scheme of $n$ Points on a Smooth Projective Surface

Arjun Paul·Ronnie Sebastian
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Abstract

Let $k$ be an algebraically closed field of characteristic $p > 3$. Let $X$ be an irreducible smooth projective surface over $k$. Fix an integer $n \geq 1$ and let ${\mathcal{H}{\it ilb}}_X^n$ be the Hilbert scheme parameterizing effective $0$-cycles of length $n$ on $X$. The aim of the present article is to find the $S$-fundamental group scheme and Nori's fundamental group scheme of the Hilbert scheme $\mathcal{H}{\it ilb}_X^n$.

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Arjun Paul, Ronnie Sebastian. 2019-07-09. Fundamental Group Schemes of Hilbert Scheme of $n$ Points on a Smooth Projective Surface. https://doi.org/10.1016/j.bulsci.2020.102898

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