## Recursive formula for $\psi ^g-\lambda _1\psi ^{g-1}+\cdots +(-1)^g\lambda _g$ in $\overline {\mathcal {M}}_{g,1}$

HTML articles powered by AMS MathViewer

- by D. Arcara and F. Sato PDF
- Proc. Amer. Math. Soc.
**137**(2009), 4077-4081 Request permission

## 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.Β 1, 13β49. MR**2120989**, DOI 10.4171/JEMS/20 - T. Graber and R. Pandharipande,
*Localization of virtual classes*, Invent. Math.**135**(1999), no.Β 2, 487β518. 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.Β 1, 1β37. 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, BirkhΓ€user Boston, Boston, MA, 1983, pp.Β 271β328. MR**717614**

## Additional 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