Frobenius splitting of Hilbert schemes of points on surfaces

Details Frobenius splitting of Hilbert schemes of points on surfaces Frobenius splitting of Hilbert schemes of points on surfaces

1999-11-23

arxiv.org/abs/math/9911181v1

Mathematics

Algebraic Geometry

Latex, 12 pages

Scientific paper

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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