Let
be a vector of integers with
. By partial resolution of the classical Abel-Jacobi map, we construct a universal twisted double ramification cycle
|
\mathsf{DR}^{\mathsf{op}}_{g,A}
|
as an operational Chow class on the Picard stack
of n-pointed genus g curves carrying a degree d line bundle. The method of construction follows the log (and b-Chow) approach to the standard double ramification cycle with canonical twists on the moduli space of curves [arXiv:1707.02261, arXiv:1711.10341, arXiv:1708.04471].
Our main result is a calculation of
|
\mathsf{DR}^{\mathsf{op}}_{g,A}
|
on the Picard stack
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 [arXiv:1812.10136]. The formula on the Picard stack is obtained from [arXiv:1812.10136] for target varieties
in the limit
. The result may be viewed as a universal calculation in Abel-Jacobi theory.
As a consequence of the calculation of
|
\mathsf{DR}^{\mathsf{op}}_{g,A}
|
on the Picard stack
, we prove that the fundamental classes of the moduli spaces of twisted meromorphic differentials in
|
\overline{\mathcal{M}}_{g,n}
|
are exactly given by Pixton's formula (as conjectured in the appendix to [arXiv:1508.07940] and in [arXiv:1607.08429]). The comparison result of fundamental classes proven in [arXiv:1909.11981] plays a crucial role in our argument. We also prove the set of relations in the tautological ring of the Picard stack
associated to Pixton's formula.
