2017/08/31 by Dhruv Ranganathan, Keli Santos-Parker, Jonathan Wise · 1 citation
Mathematics · #math.AG
paper · pdf · doi:10.2140/gt.2019.23.3315
published as Geometry & Topology 23 (2019) 3315-3366 · 37 pages, 4 figures. Final version to appear in Geometry & Topology
arxiv created 2019/03/25 · arxiv updated 2020/03/31
This is the first in a pair of papers developing a framework for the application of logarithmic structures in the study of singular curves of genus 1. We construct a smooth and proper moduli space dominating the main component of Kontsevich's space of stable genus 1 maps to projective space. A variation on this theme furnishes a modular interpretation for Vakil and Zinger's famous desingularization of the Kontsevich space of maps in genus 1. Our methods also lead to smooth and proper moduli spaces of pointed genus 1 quasimaps to projective space. Finally, we present an application to the log minimal model program for M1,n. We construct explicit factorizations of the rational maps among Smyth's modular compactifications of pointed elliptic curves.