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arXiv · 1812.06933

The Moduli Space of Stables Maps with Divisible Ramification

Oliver Leigh
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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 Fantechi-Pandharipande 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.

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Oliver Leigh. 2018-12-17. The Moduli Space of Stables Maps with Divisible Ramification. https://arxiv.org/abs/1812.06933

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