English

The $r$-ELSV Formula via Localisation on the Moduli Space of Stable Maps with Divisible Ramification

Algebraic Geometry 2020-04-16 v1

Abstract

The moduli space of stable maps with divisible ramification uses rr-th roots of a canonical ramification section to parametrise stable maps whose ramification orders are divisible by a fixed integer rr. In this article, a virtual fundamental class is constructed while letting domain curves have a positive genus; hence removing the restriction of the domain curves being genus zero. We apply the techniques of virtual localisation and obtain the rr-ELSV formula as an intersection of the virtual class with a pullback via the branch morphism.

Keywords

Cite

@article{arxiv.2004.06739,
  title  = {The $r$-ELSV Formula via Localisation on the Moduli Space of Stable Maps with Divisible Ramification},
  author = {Oliver Leigh},
  journal= {arXiv preprint arXiv:2004.06739},
  year   = {2020}
}