Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties
Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties
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加权射影空间和奇异复曲面簇中光滑完全相交的量子上同调
DOI：
10.1070/sm2007v198n09abeh003885
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发表时间：
2005
影响因子：
0.8
通讯作者：
V. Przyjalkowski
中科院分区：
文献类型：
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作者：
V. Przyjalkowski
将光滑复曲面簇中完全交的Givental定理推广到Fano簇。对于维数≥3的Fano簇，如果它们是加权射影空间或奇异环面簇中的完全交，则可以得到Gromov-Witten不变量。对这类簇也得到了一个广义Riemann-Roch方程。作为结果，计算了具有Picard群和反正则度为2，8和16的光滑Fano三重数的计数矩阵。书目：29种。
Givental's theorem for complete intersections in smooth toric varieties is generalized to Fano varieties. The Gromov-Witten invariants are found for Fano varieties of dimension ≥3 that are complete intersections in weighted projective spaces or singular toric varieties. A generalized Riemann-Roch equation is also obtained for such varieties. As a consequence, the counting matrices of smooth Fano threefolds with Picard group and anticanonical degrees 2, 8, and 16 are calculated. Bibliography: 29 titles.