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# Hodge integrals, partition matrices, and the $\lambda_g$ conjecture

Faber, C. and Pandharipande, R. (2003) Hodge integrals, partition matrices, and the $\lambda_g$ conjecture. Annals of Mathematics, 103 (1). pp. 97-124. ISSN 0003-486X. http://resolver.caltech.edu/CaltechAUTHORS:FABaom03

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## Abstract

We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via relations obtained from virtual localization in Gromov-Witten theory. An analysis of several natural matrices indexed by partitions is required.

Item Type: Article (Received October 12, 1999) We thank A. Buch, T. Graber, E. Looijenga, and R. Vakil for several related conversations. Discussions about partition matrices with D. Zagier were very helpful to us. This project grew out of previous work with E. Getzler [GeP]. His ideas have played an important role in our research. The authors were partially supported by National Science Foundation grants DMS-9801257 and DMS-9801574. C.F. thanks the Max-Planck-Institut f¨ur Mathematik, Bonn, for excellent working conditions and support, and the California Institute of Technology for hospitality during a visit in January/February 1999. CaltechAUTHORS:FABaom03 http://resolver.caltech.edu/CaltechAUTHORS:FABaom03 http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.annm/1044909496?abstract= No commercial reproduction, distribution, display or performance rights in this work are provided. 770 CaltechAUTHORS Archive Administrator 29 Sep 2005 26 Dec 2012 08:41

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