Pixton's formula and Abel-Jacobi theory on the Picard stack

Let A = (a1,...,an) be a vector of integers with (formaula presented) By partial resolution of the classical Abel–Jacobi map, we construct a universal twisted double ramification cycle DRopg,A as an operational Chow class on the Picard stack of-pointed genus- curves carrying a degree line bundle. The method of construction follows the (and b-Chow) approach to the standard double ramification cycle with canonical twists on the moduli space of curves [37], [38], [56]. Our main result is a calculation of on the Picard stack Bicg,n,d via an appropriate interpretation of Pixton’s formula in the tautological ring. The basic new tool used in the proof is the theory of double ramification cycles for target varieties [42]. The formula on the Picard stack is obtained from [42] for target varieties cpn in the limit n-> The result may be viewed as a universal calculation in Abel–Jacobi theory. As a consequence of the calculation of DRopg,Aon the Picard stack , we prove that the fundamental classes of the moduli spaces of twisted meromorphic differentials in Mg,n are exactly given by Pixton’s formula (as conjectured in [28, Appendix] and [72]). The comparison result of fundamental classes proven in [40] plays a crucial role in our argument. We also prove the set of relations in the tautological ring of the Picard stack Bicg,n,d associated with Pixton’s formula. © 2022, Verge: Studies in Global Asias. All rights reserved.