Recursive formula for $\psi ^g-\lambda _1\psi ^{g-1}+\cdots +(-1)^g\lambda _g$ in $\overline {\mathcal {M}}_{g,1}$
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- by D. Arcara and F. Sato
- Proc. Amer. Math. Soc. 137 (2009), 4077-4081
- DOI: https://doi.org/10.1090/S0002-9939-09-10018-7
- Published electronically: July 14, 2009
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Abstract:
Mumford proved that $\psi ^g-\lambda _1\psi ^{g-1}+\cdots +(-1)^g\lambda _g=0$ in the Chow ring of $\overline {\mathcal {M}}_{g,1}$. We find an explicit recursive formula for $\psi ^g-\lambda _1\psi ^{g-1}+\cdots + (-1)^g\lambda _g$ in the tautological ring of $\overline {\mathcal {M}} _{g,1}$ as a combination of classes supported on boundary strata.References
- C. Faber and R. Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. (JEMS) 7 (2005), no. 1, 13–49. MR 2120989, DOI 10.4171/JEMS/20
- T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487–518. MR 1666787, DOI 10.1007/s002220050293
- Tom Graber and Ravi Vakil, Relative virtual localization and vanishing of tautological classes on moduli spaces of curves, Duke Math. J. 130 (2005), no. 1, 1–37. MR 2176546, DOI 10.1215/S0012-7094-05-13011-3
- David Mumford, Towards an enumerative geometry of the moduli space of curves, Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser Boston, Boston, MA, 1983, pp. 271–328. MR 717614
Bibliographic Information
- D. Arcara
- Affiliation: Department of Mathematics, St. Vincent College, 300 Fraser Purchase Road, Latrobe, Pennsylvania 15650-2690
- Email: daniele.arcara@email.stvincent.edu
- F. Sato
- Affiliation: Department of Mathematics, Nagoya University Furocho, Chikusaku, Nagoya 464-8602, Japan
- Email: fumi@math.utah.edu
- Received by editor(s): August 7, 2007
- Received by editor(s) in revised form: April 26, 2009
- Published electronically: July 14, 2009
- Communicated by: Ted Chinburg
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4077-4081
- MSC (2000): Primary 14H60
- DOI: https://doi.org/10.1090/S0002-9939-09-10018-7
- MathSciNet review: 2538568