Espace des modules des faisceaux semi-stables de rang 2 et de classes de Chern $c_{1}=0$, $c_{2}=2$ et $c_{3}=0$ sur une hypersurface cubique lisse de $\mathbb{P}^{4}$

Details Espace des modules des faisceaux semi-stables de rang 2 et de classes de Chern $c_{1}=0$, $c_{2}=2$ et $c_{3}=0$ sur une hypersurface cubique lisse de $\mathbb{P}^{4}$ Espace des modules des faisceaux semi-stables de rang 2 et de classes de Chern $c_{1}=0$, $c_{2}=2$ et $c_{3}=0$ sur une hypersurface cubique lisse de $\mathbb{P}^{4}$

2000-02-08

arxiv.org/abs/math/0002058v2

Mathematics

Algebraic Geometry

12 pages, French, to appear in IMRN

Scientific paper

In this note we study the moduli space of rank two semistable sheaves on a smooth cubic hypersurface $X\subset\mathbb{P}^{4}$ with $c_{1}=0$, $c_{2}=2$ and $c_{3}=0$. 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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