Pure and Applied Mathematics Quarterly

Volume 13 (2017)

Number 4

Vanishing theorems for $(k, s)$-positive vector bundles on weakly pseudoconvex Kähler manifolds

Pages: 729 – 739

DOI: https://dx.doi.org/10.4310/PAMQ.2017.v13.n4.a6


Kai Tang (Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China)


We will use analytic methods in this paper, based on $L^2$-methods for the $\overline{\partial}$-equation, to obtain some new vanishing theorems for holomorphic vector bundles of $(k, s)$-positivity on weakly pseudoconvex Kähler manifolds which generalize those obtained by Demailly for $s$-positive vector bundles in his sense.

Received 4 November 2017

Published 21 December 2018