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Further evaluation of Wahl vanishing theorems for surface singularities in characteristic $$p$$. (English) Zbl 1442.14114
Let $$X \longrightarrow \text{Spec}(R)$$ be the minimal resolution of a rational double point defined over an algebraically closed field. Let $$E$$ be the exceptional divisor and $$S_X=\Theta_X(-\text{log }E)$$ the sheaf of logarithmic derivations. It is proved that the canonical morphism $$H^1(S_X) \longrightarrow H^1(X \setminus E,S_X)$$ is an inclusion. The dimension of $$H^1_E(S_X\otimes \mathcal O_X(E))$$ is computed. It is proved that $$H^0(X\setminus E,\Theta_X)/H^0(X,\Theta_X)$$ is isomorphic to $$H^1_E(S_X)$$ and the dimension is computed.
##### MSC:
 14J17 Singularities of surfaces or higher-dimensional varieties 32S25 Complex surface and hypersurface singularities
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##### References:
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