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


Authors: D. Arcara and F. Sato
Journal: Proc. Amer. Math. Soc. 137 (2009), 4077-4081
MSC (2000): Primary 14H60
DOI: https://doi.org/10.1090/S0002-9939-09-10018-7
Published electronically: July 14, 2009
MathSciNet review: 2538568
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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.


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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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.