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arXiv · 2208.14485

Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces

Tristan C. Collins·Yu-Shen Lin
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Abstract

We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some applications, including the Torelli theorem for $ALH^*$ gravitational instantons and explain how our results can be used to prove that all $ALH^*$ gravitational instantons can be compactified to a weak del Pezzo surface, recovering a recent result of Hein-Sun-Viaclovsky-Zhang.

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Tristan C. Collins, Yu-Shen Lin. 2022-08-30. Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces. https://arxiv.org/abs/2208.14485

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