A NOTE ON THE UNIVERSAL FAMILY OF MODULI OF STABLE SHEAVES
A NOTE ON THE UNIVERSAL FAMILY OF MODULI OF STABLE SHEAVES
复制标题
关于稳定滑轮模块通用系列的注释
DOI：
10.1515/crll.1998.026
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
K. Yoshioka
中科院分区：
文献类型：
--
作者：
K. Yoshioka
设X是C上的光滑投影曲面，H是X上的一个样本除数。设K (X)是X的Grothendieck群，K (X)在由C′-向量束生成的拓扑Grothendieck群上。对于X上的相干束E，我们用a (E)表示K (X)上的E的类。我们用H (a)表示稳定轴E的模，用H (a)表示稳定轴E的模，用H (a)表示稳定轴E的模。假设rk(a)^2。Li GL1H， GL2H计算了M H (a)的前两个Betti数，并描述了足够大的c 2 (a)时Pic（M H (a)）的结构。在本文中，我们将改写他关于Betti数的结果，并描述c2 (a)~~0的泛族存在的必要条件。
Let X be a smooth projective surface over C and H an ample divisor on X. Let K (X ) be the Grothendieck group of X and K (X ) top the topological Grothendieck group generated by C'-vector bundles. For a coherent sheaf E on X, we denote the class of E in K (X ) top by a (E ). We denote the moduli of stable sheaves E of a (E )^a by M H (a) and the Gieseker compacti cation by M H (a). Assume that rk(a)^2. Then Li GL1H, GL2H computed the rst two Betti numbers of M H (a) and described the structures of Pic(M H (a)) for su iciently large c 2 (a). In this note, we shall rewrite his results on Betti numbers and describe the necessary condition for the existence of universal family for c 2 (a)~~0.