O'Brian, Nigel Robert (1975) Zeroes of holomorphic vector fields and Grothendieck duality theory (and applications to the holomorphic fixed-point formula of Atiyah and Bott). PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Endomorphisms (Group theory), Complex manifolds , Geometry, Differential
Official Date:	April 1975
Dates:	Date Event April 1975 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Lusztig, George ; Field, M. J.
Sponsors:	Science Research Council
Extent:	73 leaves
Language:	eng

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