Bi-annual Algebraic and Tropical Meetings of
Brown and YaLE
(BATMOBYLE)

FJRW theory/Witten's top Chern classes were constructed by Fan-Jarvis-Ruan and Chang-Li-Li. The authors proved that the corresponding virtual cycles are represented by Chow cycles supported on proper loci inside non-proper moduli spaces parameterizing sections of certain line bundles. In this talk, I will focus on the example of r-spin curves to introduce a logarithmic approach using stable logarithmic maps of Abramovich-Chen-Gross-Siebert to construct a proper moduli space. This proper moduli space carries a reduced perfect obstruction theory whose associated virtual cycle is Witten’s r-spin class. Our logarithmic approach can be further applied to many interesting cases including FJRW theory, and more generally hybrid models. This is the first step toward a localization formula for higher genus invariants conjectured by Felix Janda.