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arXiv · 2112.02552

Moduli of elliptic curves in products of projective spaces

Wanlong Zheng
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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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Wanlong Zheng. 2021-12-05. Moduli of elliptic curves in products of projective spaces. https://arxiv.org/abs/2112.02552

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