Vol. 13, No. 8, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 9, 2295–2574
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Moduli of stable maps in genus one and logarithmic geometry, II

Dhruv Ranganathan, Keli Santos-Parker and Jonathan Wise

Vol. 13 (2019), No. 8, 1765–1805
DOI: 10.2140/ant.2019.13.1765

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 1. This volume focuses on logarithmic Gromov–Witten theory and tropical geometry. We construct a logarithmically nonsingular and proper 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 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 1.

logarithmic Gromov–Witten theory, tropical realizability, well spacedness condition
Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 14T05
Received: 1 September 2017
Revised: 11 May 2019
Accepted: 4 July 2019
Published: 9 October 2019
Dhruv Ranganathan
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
United Kingdom
Keli Santos-Parker
Medical School
University of Michigan
Ann Arbor, MI
United States
Jonathan Wise
Department of Mathematics
University of Colorado
Boulder, CO
United States