Powers of the theta divisor and relations in the tautological ring

Emily Clader, Samuel Grushevsky, Felix Janda, Dmitry Zakharov

Research output: Contribution to journalArticlepeer-review

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We show that the vanishing of the (g + 1)-st power of the theta divisor in the cohomology and Chow rings of the universal abelian variety implies, by pulling back along a collection of Abel–Jacobi maps, the vanishing results in the tautological ring of Mg,n of Looijenga, Ionel, Graber–Vakil, and Faber–Pandharipande. We also show that Pixton’s double ramification cycle relations, which generalize the theta vanishing relations and were recently proved by the first and third authors, imply Theorem of Graber and Vakil. Moreover, our proof provides an algorithm for expressing any tautological class on Mg,n of sufficiently high codimension as a tautological class supported on the boundary.

Original languageEnglish
Pages (from-to)7725-7754
Number of pages30
JournalInternational Mathematics Research Notices
Issue number24
StatePublished - Dec 12 2018


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