Frobenius splitting of Hilbert schemes of points on surfaces

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 Hilbn(X) of n points in X. In particular, we get the higher cohomology vanishing for ample line bundles on Hilbn(X) when X is projective and Frobenius split.

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