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Title: Zeroes of holomorphic vector fields and Grothendieck duality theory (and applications to the holomorphic fixed-point formula of Atiyah and Bott)
Author: O'Brian, Nigel Robert
ISNI:       0000 0001 3451 1595
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1975
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The holomorphic fixed-point formula of Atiyah and Bott is discussed in terms of Grothendieck's theory of duality for algebraic varieties. The treatment is valid for an endomorphism of a compact complex-analytic manifold with arbitrary isolated fixed points. An expression for the fixed-point indices is then derived for the case where the endomorphism belongs to the additive group generated by a holomorphic vector field with isolated zeroes. An application and some examples are given. Two generalisations of these results are also proved. The first deals with holomorphic vector bundles having sufficient homogeneity properties with respect to the action of the additive group on the base manifold, and the second with additive group actions on algebraic varieties.
Supervisor: Not available Sponsor: Science Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics