A complex frobenius theorem, multiplier ideal sheaves and hermitian-einstein metrics on stable bundles

Ben Weinkove*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1577-1592
Number of pages16
JournalTransactions of the American Mathematical Society
Volume359
Issue number4
DOIs
StatePublished - Apr 2007

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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