English

Properness for scaled gauged maps

Algebraic Geometry 2017-07-21 v2

Abstract

We give an algebraic proof of properness of moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt. The proof combines a git construction of Schmitt, properness for twisted stable maps by Abramovich-Vistoli, a variation of a boundedness argument due to Ciocan-Fontanine-Kim-Maulik, and a removal of singularities for bundles on surfaces in Colliot-Th\'el\`ene-Sansuc.

Keywords

Cite

@article{arxiv.1606.01383,
  title  = {Properness for scaled gauged maps},
  author = {E. González and P. Solis and C. Woodward},
  journal= {arXiv preprint arXiv:1606.01383},
  year   = {2017}
}

Comments

This was originally intended to be part of a survey for the AMS Summer Institute Proceedings, but the proof of properness grew too long and technical. The survey part [arXiv:1606.01384] was split off at the request of the editors, and is titled "Stable gauged maps". There is still substantial overlap between the two papers. This version has minor corrections

R2 v1 2026-06-22T14:17:45.753Z