Moduli of elliptic curves in products of projective spaces

2021/12/05 by Wanlong Zheng, Zheng, Wanlong
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2112.02552

openalex publication_date 2021/12/05 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We exhibit a smooth compactification of the moduli space of elliptic curves in a product of projective spaces with tangency along a subset of its toric boundary divisors. This is a Vakil--Zinger type of desingularization for maps to a product of projective spaces using ideas of elliptic singularities and logarithmic geometry, extending the recent work by Ranganathan--Santos-Parker--Wise. We use this to construct the virtual fundamental classes of the spaces of genus 1 maps to a special class of simple normal crossings pairs.

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