Oliver Leigh: The Moduli Space of Stable Maps with Divisible Ramification
Time: Wed 2019-10-09 13.15
Location: Room 3418, KTH
Lecturer: 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 rth 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.