Natural compactification of the moduli of toric pairs from the perspective of mirror symmetry

We construct a compactification of the moduli of toric pairs by using ideas from mirror symmetry. The secondary fan $\Sigma(Q)$ is used in [Ale02] to parametrize degenerations of toric pairs. It is also used in [CLS11] to control the variation of GIT. We verify the prediction of mirror symmetry that...

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Bibliographic Details
Main Author Zhu, Yuecheng
Format Journal Article
LanguageEnglish
Published 20.10.2014
Subjects
Mathematics - Algebraic Geometry
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Summary:We construct a compactification of the moduli of toric pairs by using ideas from mirror symmetry. The secondary fan $\Sigma(Q)$ is used in [Ale02] to parametrize degenerations of toric pairs. It is also used in [CLS11] to control the variation of GIT. We verify the prediction of mirror symmetry that $\Sigma(Q)$ for the moduli of toric pairs is equal to the Mori fan of the relative minimal models of the mirror family. As a result, we give an explicit construction of the compactification $\mathscr{T}_Q$ of the moduli of toric pairs which is the normalization of the compactification in [Ale02] and [Ols08].
DOI:10.48550/arxiv.1410.5393