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arXiv · 1709.00490

Moduli of stable maps in genus one and logarithmic geometry II

Dhruv Ranganathan·Keli Santos-Parker·Jonathan Wise
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Abstract

This is the second in a pair of papers developing a framework to apply logarithmic methods in the study of singular curves of genus $1$. This volume focuses on logarithmic Gromov--Witten theory and tropical geometry. We construct a logarithmically nonsingular moduli space of genus $1$ curves mapping to any toric variety. The space is a birational modification of the principal component of the Abramovich--Chen--Gross--Siebert space of logarithmic stable maps and produces an enumerative genus $1$ curve counting theory. We describe the non-archimedean analytic skeleton of this moduli space and, as a consequence, obtain a full resolution to the tropical realizability problem in genus $1$.

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Dhruv Ranganathan, Keli Santos-Parker, Jonathan Wise. 2019-07-04. Moduli of stable maps in genus one and logarithmic geometry II. https://doi.org/10.2140/ant.2019.13.1765

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