论文标题
通过量子二重性进行极端过渡
Extremal transitions via quantum Serre duality
论文作者
论文摘要
如果存在从$ z $变成奇异品种$ \ overline z $和crepant分辨率$ \ wideTilde z \ to \ overline z $，则两个品种$ z $和$ \ widetilde z $据说是由极值过渡相关的。在本文中，我们比较了零元格罗莫夫属 - 曲曲面的曲面理论，这是由福利爆炸引起的极端转变相关的。我们表明，在分析性继续和限制参数后，$ \ widetilde z $的量子$ d $ - 模块恢复了$ z $的量子$ d $ -module。该证明为定理中出现的分析延续和限制参数提供了几何解释。
Two varieties $Z$ and $\widetilde Z$ are said to be related by extremal transition if there exists a degeneration from $Z$ to a singular variety $\overline Z$ and a crepant resolution $\widetilde Z \to \overline Z$. In this paper we compare the genus-zero Gromov--Witten theory of toric hypersurfaces related by extremal transitions arising from toric blow-up. We show that the quantum $D$-module of $\widetilde Z$, after analytic continuation and restriction of a parameter, recovers the quantum $D$-module of $Z$. The proof provides a geometric explanation for both the analytic continuation and restriction parameter appearing in the theorem.
