Closed-String Mirror Symmetry for Log Calabi-Yau Surfaces

Hyunbin Kim
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Abstract

This paper establishes closed-string mirror symmetry for all log Calabi-Yau surfaces with generic parameters, where the exceptional divisor are sufficiently small. We demonstrate that blowing down a $(-1)$-divisor removes a single geometric critical point, ensuring that the resulting potential remains a Morse function. Additionally, we show that the critical values are distinct, which implies that the quantum cohomology $QH^{\ast}(X)$ is semi-simple.
对数 Calabi-Yau 曲面的闭弦镜像对称性
本文为具有一般参数的所有对数卡拉比-优素福曲面建立了闭弦镜像对称性,其中特殊除数足够小。我们证明,向下吹$(-1)$除数可以消除单个几何临界点,从而确保所得到的势仍然是莫尔斯函数。此外,我们还证明了临界值是不同的,这意味着量子同调 $QH^{\ast}(X)$ 是半简单的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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