Degree-three spin Hurwitz numbers (Q2393599)

Spin Hurwitz numbers count ramified covers of a surface endowed with a theta characteristic. They are closely related to dimension-zero relative Gromov-Witten invariants of Kähler surfaces. \textit{A. Eskin, A. Okounkov} and \textit{R. Pandharipande} [Adv. Math. 217, No. 3, 873--888 (2008; Zbl 1157.14014)] proved a formula for the spin Hurwitz numbers in genus one in terms of the combinatorics of the Sergeev group. In this paper, the author proved a recursion formula for degree-three spin Hurwitz numbers by exploiting degeneration techniques of relative Gromov-Witten theory. It has been generalized to higher degrees by the author and \textit{Th. H. Parker} [``Recursion Formulas for Spin Hurwitz Numbers'', \url{arXiv:1212.1825}].