A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles

Author:
Ben Weinkove

Journal:
Trans. Amer. Math. Soc. **359** (2007), 1577-1592

MSC (2000):
Primary 53C07

DOI:
https://doi.org/10.1090/S0002-9947-06-03985-7

Published electronically:
October 16, 2006

MathSciNet review:
2272141

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Abstract | References | Similar Articles | Additional Information

Abstract: A complex Frobenius theorem is proved for subsheaves of a holomorphic vector bundle satisfying a finite generation condition and a differential inclusion relation. A notion of `multiplier ideal sheaf' for a sequence of Hermitian metrics is defined. The complex Frobenius theorem is applied to the multiplier ideal sheaf of a sequence of metrics along Donaldson's heat flow to give a construction of the destabilizing subsheaf appearing in the Donaldson-Uhlenbeck-Yau theorem, in the case of algebraic surfaces.

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Additional Information

**Ben Weinkove**

Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

DOI:
https://doi.org/10.1090/S0002-9947-06-03985-7

Received by editor(s):
January 18, 2005

Published electronically:
October 16, 2006

Additional Notes:
This work was carried out while the author was a Ph.D. student at Columbia University, supported by a graduate fellowship.

Article copyright:
© Copyright 2006
American Mathematical Society