Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces
Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces
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DOI：
10.1016/j.aim.2006.03.006
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发表时间：
2004-06
影响因子：
1.7
通讯作者：
E. Markman
中科院分区：
文献类型：
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作者：
E. Markman
设M为具有有效（或平凡）反正则线束的射影曲面S上稳定相干束的光滑紧模空间。我们找到了M的上同环具有积分系数的生成子。当S是单连通且在S×M上存在一个泛束E时，则其类[E]在拓扑k环的张量积Ktop0(S)⊗Ktop0(M)中允许k<s:1>第n次分解。生成器是Ktop0(M)中[E]的k<s:1> n次因子的chen类。一般情况是相似的。
Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf E exists over S×M, then its class [E] admits a Künneth decomposition as a class in the tensor product Ktop0(S)⊗Ktop0(M) of the topological K-rings. The generators are the Chern classes of the Künneth factors of [E] in Ktop0(M). The general case is similar.