2014/08/12 by Yuecheng Zhu, Zhu, Yuecheng
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1408.2676
openalex publication_date 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that Martin Olsson's compactification of moduli space of polarized abelian varieties in \citeols08 can be interpreted in terms of KSBA stable pairs. We find that there is a canonical set of divisors S(K2) associated with each cusp. Near the cusp, a polarized semiabelic scheme (X, G,L) is the canonical degeneration given by the compactification if and only if (X,G,Θ) is an object in \mathscrAPg,d for any Θ∈ S(K2). Moreover, we give an alternative construction of the compactification by using mirror symmetry. We construct a toroidal compactification \mathscrAg,δm that is isomorphic to Olsson's compactification over characteristic zero. The data needed for a toroidal compactification is a collection of fans. We obtain the collection of fans from the Mori fans of the minimal models of the mirror families.