Sur la cohomologie d'un fibre tautologique sur le schema de Hilbert\n d'une surface

1999/04/01 by Gentiana Danila, Danila, Gentiana · 1 citation
Mathematics · #14C05 #14F17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.math/9904004

openalex publication_date 1999/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the cohomology spaces for the tautological bundle tensor the\ndeterminant bundle on the punctual Hilbert scheme H of subschemes of length n\nof a smooth projective surface X. We show that for L and A invertible vector\nbundles on X, and w the canonical bundle of X, if w^-1\⊗ L,\nw^-1\⊗ A and A are ample vector bundles, then the higher cohomology\nspaces on H of the tautological bundle associated to L tensor the determinant\nbundle associated to A vanish, and the space of global sections is computed in\nterms of H⁰(A) and H⁰(L\⊗ A). This result is motivated by the\ncomputation of the space of global sections of the determinant bundle on the\nmoduli space of rank 2 semi-stable sheaves on the projective plane, supporting\nLe Potier's Strange duality conjecture on the projective plane.\n

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