The Torelli theorem for ALH∗ gravitational instantons

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First author draft
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Lin, Yu-Shen
Collins, Tristan
Jacob, Adam
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Y.-.S. Lin, T. Collins, A. Jacob. "The Torelli Theorem for ALH∗ Gravitational Instantons." https://arxiv.org/abs/2111.09260
Abstract
We give a short proof of the Torelli theorem for ALH∗ gravitational instantons, using the authors' previous construction of mirror special Lagrangian fibrations in del Pezzo surfaces and rational elliptic surfaces together with recent work of Sun-Zhang. In particular, this includes an identification of 10 diffeomorphism types of ALH∗b gravitational instantons.
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