Properties of Rational Singularities
Let f : X → Y be a desingularization of a normal singularity (Y, y), with Y an affine surface, E1, ... , En the irreducible components of the reduced fiber E = f−1(y)red, and L an invertible OX-module such that (L · Ei) ≥ (ωX · Ei), i = 1, ... , n. Then H1(X, L) = 0.
KeywordsExact Sequence Irreducible Component Local Ring Rational Singularity Normal Singularity
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