Ricci-flat Deformations of Holomorphic Vector Bundles

Details Ricci-flat Deformations of Holomorphic Vector Bundles Ricci-flat Deformations of Holomorphic Vector Bundles

2007-01-19

arxiv.org/abs/math/0701538v2

Mathematics

Algebraic Geometry

13 pages; Thm 6.6. corrected, more examples included

Scientific paper

In this paper we give a criterion for a deformation of a hermitian vector bundle to be Ricci-flat. As an application we show that on a K\"ahler manifold, every deformation of a vector bundle can be made Ricci-flat whereas on some Hopf manifolds, the non-existence of a Ricci-flat deformation is related to non-trivial vector bundles on the universal cover ${\mathbb C}^n\setminus\{0\}$. On a surface with $b_1(X)\not=0$ filtrable Ricci-rigid vector bundles prove to be very special. We apply this to Inoue and Hopf surfaces.

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