2014/10/20 by Yuecheng Zhu, Zhu, Yuecheng
Mathematics · #14M25 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14M25
paper · pdf · doi:10.48550/arxiv.1410.5393
28 pages. Comments are welcome
openalex publication_date 2014/10/20 · arxiv created 2016/09/13 · arxiv updated 2016/09/14 · openalex created_date 2016/09/23 · openalex updated_date 2026/07/28
We construct a compactification of the moduli of toric pairs by using ideas from mirror symmetry. The secondary fan Σ(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 Σ(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 \mathscrTQ of the moduli of toric pairs which is the normalization of the compactification in [Ale02] and [Ols08].