Elliptic genera of toric varieties and applications to mirror symmetry
Elliptic genera of toric varieties and applications to mirror symmetry
复制标题
复曲面簇的椭圆属及其在镜像对称中的应用
DOI：
10.1007/s002220000058
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发表时间：
1999
影响因子：
3.1
通讯作者：
A. Libgober
中科院分区：
文献类型：
--
作者：
L. Borisov;A. Libgober
文摘：本文证明了Calabi-Yau流形的椭圆亏格是Jacobi形式，发现在哪些维数上椭圆亏格由Hodge数决定，并证明了复曲面簇中的Calabi-Yau超曲面的椭圆亏格与其镜像重合.镜像性质的证明是基于椭圆亏格到具有Gorenstein奇点的复曲面簇中的Calabi-Yau超曲面的扩张。
Abstract.The paper contains a proof that elliptic genus of a Calabi-Yau manifold is a Jacobi form, finds in which dimensions the elliptic genus is determined by the Hodge numbers and shows that elliptic genera of a Calabi-Yau hypersurface in a toric variety and its mirror coincide up to sign. The proof of the mirror property is based on the extension of elliptic genus to Calabi-Yau hypersurfaces in toric varieties with Gorenstein singularities.