arXiv 1809.047142018-09hep-thmath.AG

Calabi-Yau广义完全交与层的上同调

Calabi-Yau generalized complete intersections and aspects of cohomology of sheaves

Qiuye Jia, Hai Lin

备注：: 40 pages. Journal version
发表信息：: J.Math.Phys. 61 (2020) 5, 052301
DOI：: 10.1063/1.5058139

摘要：

我们考虑了射影空间的乘积空间中的广义完全交流形，并研究了其上层的上同调。首先，我们给出并证明了射影空间的周围积空间的子簇的层的上同调群的消失定理。然后，我们证明了配置矩阵之间的等价性完全相交的卡-丘流形。给出了广义完备交流形中曲线的亏格公式。这些曲线中的一些出现作为某些对称群作用在广义完全相交的Calabi-Yau流形上的不动点轨迹。我们还沿着曲线做了一个爆破，由此可以生成新的Calabi-Yau流形。利用谱序列方法计算了广义完全交Calabi-Yau流形的Hodge数及其曲线的亏格。

英文摘要：

We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the cohomology groups of sheaves for subvarieties of the ambient product space of projective spaces. We then prove an equivalence between configuration matrices of complete intersection Calabi-Yau manifolds. We also present a formula of the genus of curves in generalized complete intersection manifolds. Some of these curves arise as the fixed point locus of certain symmetry group action on the generalized complete intersection Calabi-Yau manifolds. We also make a blowing-up along the curves, by which one can generate new Calabi-Yau manifolds. Moreover, an approach on spectral sequences is used to compute Hodge numbers of generalized complete intersection Calabi-Yau manifolds and the genus of curves therein.

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