UNSPECIFIED (2001) Cohomology of a tautological bundle on the Hilbert scheme of a surface. JOURNAL OF ALGEBRAIC GEOMETRY, 10 (2). pp. 247-280. ISSN 1056-3911

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Abstract

We compute the cohomology spaces for the tautological bundle tensor the determinant bundle on the punctual Hilbert scheme X-[m] of a smooth projective surface X on C. We show that for L vector bundle and A invertible vector bundle on X, if H-q(X, A) = H-q(X, L x A) = 0 for q greater than or equal to 1, then the higher cohomology spaces on X-[m] of the tautological bundle associated to L tensor the determinant bundle associated to A vanish, and the space of global sections is computed in terms of H-0(A) and H-0(X, L x A). This result is motivated by the computation of the space of global sections of the determinant bundle on the moduli space of rank 2 semi-stable sheaves on the projective plane, supporting Le Potier's strange duality conjecture on the projective plane.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	JOURNAL OF ALGEBRAIC GEOMETRY
Publisher:	AMER MATHEMATICAL SOC
ISSN:	1056-3911
Date:	April 2001
Volume:	10
Number:	2
Number of Pages:	34
Page Range:	pp. 247-280
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/12383

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