A modular compactification of \M_1,n from\n A_\∞-structures

2014/08/04 by Yankı Lekili, Lekili, Yanki, Alexander Polishchuk +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1408.0611

openalex publication_date 2014/08/04 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28

Abstract

We show that a certain moduli space of minimal A_\∞-structures\ncoincides with the modular compactification \\M_1,n(n-1) of\n\M_1,n constructed by Smyth. In addition, we describe these moduli\nspaces and the universal curves over them by explicit equations, prove that\nthey are normal and Gorenstein, show that their Picard groups have no torsion\nand that they have rational singularities if and only if n\≤ 11.\n

Citations

• Arithmetic mirror symmetry for the 2-torus

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