Ricci-flat Deformations of Holomorphic Vector Bundles
Abstract
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 Kähler 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 2007
- DOI:
- 10.48550/arXiv.math/0701538
- arXiv:
- arXiv:math/0701538
- Bibcode:
- 2007math......1538K
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14J60
- E-Print:
- 13 pages