Variétés de modules alternatives
Variétés de modules alternatives
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DOI：
10.5802/aif.1669
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发表时间：
1998
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影响因子：
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通讯作者：
J. Drézet
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文献类型：
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作者：
J. Drézet
设X是射影不可约光滑代数簇。X上的层“细模空间”是X上的凝聚层族F，其参数化为：F在M上平坦，对M的所有不同点x，y，X上的层F_x，F_y不同构，F是F_x的完全变形；F具有明显的局部普适性。我们还定义了一个“局部定义的精细模空间”，其中F被一个族(F_I)代替，其中F_i定义在M的开子集U_i上，U_i覆盖M。本文致力于研究这种精细模空间。我们首先给出了一些一般性的结果，并将它们应用于射影平面上的三种情况：先验层的细模空间，由单秩1层构成的细模空间，以及由态射的模空间得到的模空间。在第一种情况下，我们给出了局部定义但不是全局定义的细模空间的一个例子，在第二种情况下，我们给出了一个极大的非投射细模空间的例子，在第三种情况下，我们发现了一个由简单无挠层组成的射影细模空间，它包含稳定的层，但不同于相应的稳定层的模空间。
Let X be a projective irreducible smooth algebraic variety. A "fine moduli space" of sheaves on X is a family F of coherent sheaves on X parametrized by an integral variety M such that : F is flat on M; for all distinct points x, y of M the sheaves F_x, F_y on X are not isomorphic and F is a complete deformation of F_x; F has an obvious local universal property. We define also a "fine moduli space defined locally", where F is replaced by a family (F_i), where F_i is defined on an open subset U_i of M, the U_i covering M. This paper is devoted to the study of such fine moduli spaces. We first give some general results, and apply them in three cases on the projective plane : the fine moduli spaces of prioritary sheaves, the fine moduli spaces consisting of simple rank 1 sheaves, and those which come from moduli spaces of morphisms. In the first case we give an exemple of a fine moduli space defined locally but not globally, in the second an exemple of a maximal non projective fine moduli space, and in the third we find a projective fine moduli space consisting of simple torsion free sheaves, containing stable sheaves, but which is different from the corresponding moduli space of stable sheaves.