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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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