对数 Calabi-Yau 曲面的闭弦镜像对称性

arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-05 DOI:arxiv-2408.02592

Hyunbin Kim

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引用次数: 0

摘要

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。

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Closed-String Mirror Symmetry for Log Calabi-Yau Surfaces

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.

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arXiv - MATH - Symplectic Geometry

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