Mathematics – Algebraic Geometry
Scientific paper
1999-04-01
Mathematics
Algebraic Geometry
27 pages, part of PhD thesis
Scientific paper
We compute the cohomology spaces for the tautological bundle tensor the determinant bundle on the punctual Hilbert scheme H of subschemes of length n of a smooth projective surface X. We show that for L and A invertible vector bundles on X, and w the canonical bundle of X, if $w^{-1}\otimes L$, $w^{-1}\otimes A$ and A are ample vector bundles, then the higher cohomology spaces on H 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 $H^0(L\otimes A)$. 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.
No associations
LandOfFree
Sur la cohomologie d'un fibre tautologique sur le schema de Hilbert d'une surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Sur la cohomologie d'un fibre tautologique sur le schema de Hilbert d'une surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sur la cohomologie d'un fibre tautologique sur le schema de Hilbert d'une surface will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-110195