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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: 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

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