# Oliver Leigh: The Moduli Space of Stable Maps with Divisible Ramification

**Time: **
Wed 2019-10-09 13.15

**Location: **
Room 3418, KTH

**Participating: **
Oliver Leigh, Stockholm University

Abstract: In this talk we discuss a theory of stable maps 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 construct a natural moduli space parametrising these objects and explore its enumerative geometry. This includes an analogue of the Fantechi–Pandharipande branch morphism and a virtual fundamental class compatible with that of the space of stable maps. This theory is anticipated to have applications to *r*-spin Hurwitz theory. In particular, it is expected to provide a geometric proof of the *r*-ELSV formula.