Espace des modules des faisceaux semi-stables de rang 2 et de classes de Chern c₁=0, c₂=2 et c₃=0 sur une hypersurface cubique lisse de ℙ⁴

2000/02/08 by Stéphane Druel, Druel, Stéphane
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.math/0002058

12 pages, French, to appear in IMRN

openalex publication_date 2000/02/08 · arxiv created 2000/05/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we study the moduli space of rank two semistable sheaves on a smooth cubic hypersurface X⊂ℙ⁴ with c₁=0, c₂=2 and c₃=0. We show that it is isomorphic to the blow-up of the intermediate jacobian J(X) of X along the Fano surface of X. We complete previous results of Iliev-Markushevich AG/9910058 and Markushevich-Tikhomirov AG/9910063.

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