Polynomiality of the double ramification cycle

Let A = (a 1 , . . ., a n ) ∈ Z n be a sequence with sum k(2g-2+n).The double ramification cycle DR g (A) ∈ CH g M g,n is the virtual class of the locus of curves (C, p 1 , . . ., p n ) where the line bundle ω log C -k a i p i is trivial.Although there has long been a formula for DR g (A), the exact dependence on A was unknown for a long time, though it was conjectured to be polynomial in A. A proof was announced by Janda, Pandharipande, Pixton, and Zvonkine in 2017, and Pixton gave a proof incorporating ideas of Zagier in 2023.Here we present an alternative proof of the polynomiality of the double ramification cycle.