Green, Howard Ivor (1980) Chern classes for coherent sheaves. PhD thesis, University of Warwick.

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Abstract

We present in this paper a construction of Chern classes
for a coherent sheaf S on a complex manifold X. In fact we
construct classes Cp(S) in H2p(X, C), depending only on the
smooth equivalence class of the sheaf S. and analytic classes
CAp(S) in Hp(X, Ωp) (Ωp denotes the sheaf of germs of holomorphic
p-forms on X). We show that these invariants extend the classical
and Atiyah constructions for locally free sheaves, and that the
analytic class CAp(S) is the 'leading term' of type (p, p) in the
expansion by type of Cp(S). In the case of a compact manifold,
we are able to show that the classes Cp(S) correspond (up to a
constant factor) with those defined by Atiyah and Hirzebruch in
[2]. Thus in particular the Cp(S) are integral cohomology classes.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Chern classes, Sheaf theory, Complex manifolds
Official Date:	January 1980
Dates:	Date Event January 1980 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	O'Brian, Nigel Robert, 1948- ; Eells, James, 1926-2007
Extent:	51 p.
Language:	eng

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