2017/09/30 by Dhruv Ranganathan, Keli Santos-Parker, Jonathan Wise · 18 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Genus #Invertible matrix #Logarithm #Modular equation #Moduli of algebraic curves #Moduli space #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Realizability #math.AG
paper · pdf · doi:10.2140/ant.2019.13.1765
published in Algebra & Number Theory 13(8), 1765-1805 (Mathematical Sciences Publishers) · 36 pages, 5 figures. Final version to appear in Algebra & Number Theory
openalex created_date 2017/08/17 · arxiv created 2019/07/04 · openalex publication_date 2019/10/09 · arxiv updated 2019/10/16 · openalex updated_date 2026/08/05
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 [math] . This volume focuses on logarithmic Gromov–Witten theory and tropical geometry. We construct a logarithmically nonsingular and proper moduli space of genus [math] 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 [math] .