Frobenius splitting of Hilbert schemes of points on surfaces

1999/11/23 by Shrawan Kumar, Kumar, Shrawan, Jesper Funch Thomsen +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/9911181

Latex, 12 pages

arxiv created 1999/11/23 · arxiv updated 2009/11/30

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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