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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
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

F. Sato
Affiliation: Department of Mathematics, Nagoya University Furocho, Chikusaku, Nagoya 464-8602, Japan

PII: S 0002-9939(09)10018-7
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.

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