Existence of holomorphic sections and perturbation of positive line bundles over $q$--concave manifolds

Details Existence of holomorphic sections and perturbation of positive line bundles over $q$--concave manifolds Existence of holomorphic sections and perturbation of positive line bundles over $q$--concave manifolds

2004-02-03

arxiv.org/abs/math/0402041v1

Mathematics

Complex Variables

18 pages, AmsTex

Scientific paper

By using asymptotic Morse inequalities we give a lower bound for the space of holomorphic sections of high tensor powers in a positive line bundle over a q-concave domain. The curvature of the positive bundle induces a hermitian metric on the manifold. The bound is given explicitely in terms of the volume of the domain in this metric and a certain integral on the boundary involving the defining function and its Levi form. As application we study the perturbattion of the complex structure of a q-concave manifold.

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