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Points non factoriels des variétés de modules de faisceaux semi- stables sur une surface rationnelle. (Non factorial points of moduli varieties of semi-stable sheaves on a rational surface). (French) Zbl 0711.14029
Let X be a projective smooth rational surface over $${\mathbb{C}}$$, $${\mathcal O}_ X(1)$$ a very ample line bundle on X such that $$K_ X.{\mathcal O}_ X(1)<0$$. The main subject of this paper is the factoriality of the local rings of the closed points of moduli varieties of semi-stable sheaves on X (with respect to $${\mathcal O}_ X(1)).$$
Two types of points are introduced. In some cases, the local rings of points of type 1 are factorial, but the local rings of points of type 2 are never factorial. In the case of $${\mathbb{P}}_ 1\times {\mathbb{P}}_ 1$$, for rank-2 sheaves with $$c_ 1=0$$, it is possible to determine precisely which points have a factorial local ring.
Reviewer: J.-M.Drezet

##### MSC:
 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14M20 Rational and unirational varieties 14J10 Families, moduli, classification: algebraic theory 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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