Mumford's formula on the universal Picard stack

Alessandro Chiodo; David Holmes

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arXiv · 2309.00315

Mumford's formula on the universal Picard stack

Alessandro Chiodo·David Holmes

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Abstract

We construct a derived pushforward of the r-th root of the universal line bundle over the Picard stack of genus g prestable curves carrying a line bundle. We prove a number of basic properties, and give a formula in terms of standard tautological generators. After pullback, our formula recovers formulae of Mumford, of the first-named author, and of Pagani--Ricolfi--van Zelm. We apply these constructions to prove a conjecture expressing the coefficients of higher powers of r in the so-called `Chiodo classes' to the double ramification cycle, and to give a formula for the r-spin logarithmic double ramification cycle.

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Alessandro Chiodo, David Holmes. 2023-09-01. Mumford's formula on the universal Picard stack. https://arxiv.org/abs/2309.00315

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