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- W2014362531 abstract "The first goal of the article is to solve several fundamental problems in the theory of holomorphic bundles over non-algebraic manifolds: For instance we prove that stability and semi-stability are Zariski open properties in families when the Gauduchon degree map is a topological invariant, or when the parameter manifold is compact. Second we show that, for a generically stable family of bundles over a Kahler manifold, the Petersson-Weil form extends as a closed positive current on the whole parameter space of the family. This extension theorem uses classical tools from Yang-Mills theory developed by Donaldson (e.g. the Donaldson functional and the heat equation for Hermitian metrics on a holomorphic bundle). We apply these results to study families of bundles over a Kahlerian manifold $Y$ parameterized by a non-Kahlerian surface $X$, proving that such families must satisfy very restrictive conditions. These results play an important role in our program to prove existence of curves on class VII surfaces." @default.
- W2014362531 created "2016-06-24" @default.
- W2014362531 creator A5027490031 @default.
- W2014362531 date "2007-04-19" @default.
- W2014362531 modified "2023-09-27" @default.
- W2014362531 title "Families of holomorphic bundles" @default.
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