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arXiv · 2112.07504

Torelli-type theorems for gravitational instantons with quadratic volume growth

Gao Chen·Jeff Viaclovsky·Ruobing Zhang
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Abstract

We prove Torelli-type uniqueness theorems for both ALG$^*$ gravitational instantons and ALG gravitational instantons which are of order $2$. That is, the periods uniquely characterize these types of gravitational instantons up to diffeomorphism. We define a period mapping $\mathscr{P}$, which we show is surjective in the ALG cases, and open in the ALG$^*$ cases. We also construct some new degenerations of hyperk\"ahler metrics on the K3 surface which exhibit bubbling of ALG$^*$ gravitational instantons.

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BibTeXRIS

Gao Chen, Jeff Viaclovsky, Ruobing Zhang. 2021-12-14. Torelli-type theorems for gravitational instantons with quadratic volume growth. https://arxiv.org/abs/2112.07504

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