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Mathematics > Algebraic Geometry

arXiv:1812.06933 (math)
[Submitted on 17 Dec 2018]

Title:The Moduli Space of Stables Maps with Divisible Ramification

Authors: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.
Comments: 29 pages
Subjects: Algebraic Geometry (math.AG); Mathematical Physics (math-ph)
MSC classes: 14D23, 14H10, 14N35
Cite as: arXiv:1812.06933 [math.AG]
  (or arXiv:1812.06933v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.06933

Submission history

From: Oliver Leigh [view email]
[v1] Mon, 17 Dec 2018 18:16:42 UTC (41 KB)
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