Dhruv Ranganathan, Keli Santos-Parker and Jonathan
Wise
Vol. 13 (2019), No. 8, 1765–1805
DOI: 10.2140/ant.2019.13.1765
Abstract
This is the second in a pair of papers developing a framework to apply
logarithmic methods in the study of stable maps and singular curves of genus
. This
volume focuses on logarithmic Gromov–Witten theory and tropical geometry. We
construct a logarithmically nonsingular and proper moduli space of genus
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 logarithmic analogues of Vakil
and Zinger’s genus one reduced Gromov–Witten theory. We describe the
nonarchimedean analytic skeleton of this moduli space and, as a consequence,
obtain a full resolution to the tropical realizability problem in genus
.
Keywords
logarithmic Gromov–Witten theory, tropical realizability,
well spacedness condition