arXiv subjects
Publications and source records attributed to Jesper Funch Thomsen.
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.
We use the G-invariant non-degenerate form on the Steinberg module to Frobenius split the cotangent bundle of a flag variety in good prime characteristics. This was previously only known for the general linear group. Applications are a vanishing theorem for pull back of line bundles to the cotangent bundle (proved for the classical groups and G_2 by Andersen and Jantzen and in characteristic zero by B. Broer (for all groups)), normality and rational singularities for the subregular nilpotent variety and good filtrations of the global sections of pull backs of line bundles to the cotangent bundle, which in turn implies good filtrations of cohomology of induced representations.
Let G be a linear algebraic group, P be a parabolic subgroup of G and βbe a cycle of dimension 1 in the Chow group of the quotient G/P. Using geometric arguments and Borel's fixed point theorem, we prove that the moduli space \bar{M}_{0,n}(G/P, β) of n-pointed genus 0 stable maps representing βis irreducible.