Duke Mathematical Journal

The structure of the tautological ring in genus one

Dan Petersen

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 12 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1394630554

Digital Object Identifier
doi:10.1215/00127094-2429916

Mathematical Reviews number (MathSciNet)
MR3178432

Zentralblatt MATH identifier
1291.14045

Subjects
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]

Citation

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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