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Frobenius splitting of Hilbert schemes of points on surfaces

Shrawan Kumar·Jesper Funch Thomsen
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Abstract

Let X be a quasiprojective smooth surface defined over an algebraically closed field of positive characteristic. We show that if X is Frobenius split then so is the Hilbert scheme Hilb^n(X) of n points in X. In particular, we get the higher cohomology vanishing for ample line bundles on Hilb^n(X) when X is projective and Frobenius split.

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Shrawan Kumar, Jesper Funch Thomsen. 1999-11-23. Frobenius splitting of Hilbert schemes of points on surfaces. https://arxiv.org/abs/math/9911181

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