Cohomology of a tautological bundle on the Hilbert scheme of a surface
UNSPECIFIED. (2001) Cohomology of a tautological bundle on the Hilbert scheme of a surface. JOURNAL OF ALGEBRAIC GEOMETRY, 10 (2). pp. 247-280. ISSN 1056-3911Full text not available from this repository.
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|
|Number of Pages:||34|
|Page Range:||pp. 247-280|
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