Duke Mathematical Journal

The structure of the tautological ring in genus one

Dan Petersen

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We prove Getzler’s claims about the cohomology of the moduli space of stable curves of genus one, that is, that the even cohomology ring is spanned by the strata classes and that all relations between these classes follow from the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) relation and Getzler’s relation. In particular, the even cohomology ring is isomorphic to the tautological ring.

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Duke Math. J., Volume 163, Number 4 (2014), 777-793.

First available in Project Euclid: 12 March 2014

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Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]


Petersen, Dan. The structure of the tautological ring in genus one. Duke Math. J. 163 (2014), no. 4, 777--793. doi:10.1215/00127094-2429916. https://projecteuclid.org/euclid.dmj/1394630554

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