Moduli of curves of genus one with twisted fields

We construct a smooth Artin stack parameterizing the stable weighted curves of genus one with twisted fields and prove that it is isomorphic to the blowup stack of the moduli of genus one weighted curves studied by Hu and Li. This leads to a blowup-free construction of Vakil–Zinger’s desingularization of the moduli of genus one stable maps to projective spaces. This construction provides the cornerstone of the theory of stacks with twisted fields, which is thoroughly studied in [8] and leads to a blowup-free resolution of the stable map moduli of genus two.

Keywords

moduli of weighted curves, twisted fields, blowup-free desingularization

2010 Mathematics Subject Classification

14D23, 14E15

The full text of this article is unavailable through your IP address: 172.17.0.1

Received 4 June 2020

Accepted 31 March 2021

Published 6 July 2022