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 -