TY - JOUR

T1 - A complex frobenius theorem, multiplier ideal sheaves and hermitian-einstein metrics on stable bundles

AU - Weinkove, Ben

PY - 2007/4

Y1 - 2007/4

N2 - 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.

AB - 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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U2 - 10.1090/S0002-9947-06-03985-7

DO - 10.1090/S0002-9947-06-03985-7

M3 - Article

AN - SCOPUS:77950998282

SN - 0002-9947

VL - 359

SP - 1577

EP - 1592

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 4

ER -