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Mumford's formula on the universal Picard stack | | Alessandro Chiodo
; David Holmes
; | | Date: |
1 Sep 2023 | | 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. | | Source: | arXiv, 2309.00315 | | Services: | Forum | Review | PDF | Favorites | |
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