Cohomology vanishing theorems on weakly 1-complete manifolds (Q792516): Difference between revisions

A survey article on the vanishing theorems on weakly 1-complete manifolds which are obtained mainly in the 70's by S. Nakano, O. Abdelkader, etc., based on the \(L^ 2\)-method of Andreotti-Vesentini. A new and simple proof is given to Nakano's vanishing theorem for the cohomology group of bi-degree (p,q) with coefficients in positive line bundles. Applications to classical problems such as the inverse of monoidal transformation are given, but not in detail. In sublemma 2, there is a misprint. \(''\{c_ k\}_{k\geq m}\) is monotonically decreasing'' should read \(''\{c_ k^{1/k}\}_{k\geq m}\) is monotonically decreasing''.