Frobenius splitting of Hilbert schemes of points on surfaces
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Let X be a quasiprojective smooth surface defined over an algebraically closed field of positive characteristic. In this note we show that if X is Frobenius split then so is the Hilbert scheme Hilb\(^n(X)\) of n points inX. In particular, we get the higher cohomology vanishing for ample line bundles on Hilb\(^n(X)\) when X is projective and Frobenius split.
KeywordsSmooth Surface Line Bundle Positive Characteristic Hilbert Scheme Ample Line Bundle
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