The Moduli Space of Stables Maps with Divisible Ramification
Abstract
We develop a theory for stable maps to curves with divisible ramification. For a fixed integer $r>0$, we show that the condition of every ramification locus being divisible by $r$ is equivalent to the existence of an $r$th root of a canonical section. We consider this condition in regards to both absolute and relative stable maps and construct natural moduli spaces in these situations. We construct an analogue of the FantechiPandharipande branch morphism and when the domain curves are genus zero we construct a virtual fundamental class. This theory is anticipated to have applications to $r$spin Hurwitz theory. In particular it is expected to provide a proof of the $r$spin ELSV formula [SSZ'15, Conj. 1.4] when used with virtual localisation.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 arXiv:
 arXiv:1812.06933
 Bibcode:
 2018arXiv181206933L
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematical Physics;
 14D23;
 14H10;
 14N35
 EPrint:
 29 pages