Description
The purpose of this talk is to present computations of certain cycles on the moduli space of stable curves M_{g,n}(bar) arising from differentials and spin structures on curves. In the first part, I will provide a brief introduction to the moduli spaces of curves, tautological rings, and related moduli spaces. In the second part, we will focus on specific loci in M_{g,n}(bar), called strata of k-differentials, which parametrize stable curves admitting a k-differential with prescribed zeros and poles. A natural question is whether there is an explicit formula in the Chow ring of M_{g,n}(bar) for the Chow classes of these loci. When k and all the prescribed orders of zeros and poles are odd, we can define the so-called “spin refinement” of this problem. We will investigate an approach to these problems via (spin) double ramification cycles and demonstrate how they can be used to obtain formulas for the classes of strata of k-differentials and their spin refinements.
This talk is based on joint works Adrien Sauvaget and David Holmes.
The first 45 minutes of the seminar will be dedicated to providing some background and an introduction to the topic.
People who are interested but unable to attend in person will have the opportunity to join us via Zoom.
Join Zoom Meeting
https://cs-uni-saarland-de.zoom.us/j/89831969880?pwd=Qj5U82SPUV6UbqSFkbqvicraV9dQXz.1
Meeting chat link
https://cs-uni-saarland-de.zoom.us/launch/jc/89831969880
Meeting ID: 898 3196 9880
Passcode: 296498