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Euler characteristics of universal cotangent line bundles on $ \overline{\mathcal{M}}_{1,n}$


Authors: Y.-P. Lee and F. Qu
Journal: Proc. Amer. Math. Soc. 142 (2014), 429-440
MSC (2010): Primary 14H10; Secondary 14J15, 14D23, 14D22, 14H15
DOI: https://doi.org/10.1090/S0002-9939-2013-11800-9
Published electronically: November 5, 2013
MathSciNet review: 3133985
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an effective algorithm to compute the Euler characteristics $ \chi (\overline {\mathcal {M}}_{1,n}, \bigotimes _{i=1}^n L_i^{ d_i})$. This work is a sequel to the 1997 work of the first author.

In addition, we give a simple proof of Pandharipande's vanishing theorem $ H^j (\overline {\mathcal {M}}_{0,n}, \bigotimes _{i=1}^n L_i^{ d_i})=0$ for $ j \ge 1, d_i \ge 0$.


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Additional Information

Y.-P. Lee
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
Email: yplee@math.utah.edu

F. Qu
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
Email: qu@math.utah.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11800-9
Received by editor(s): December 29, 2011
Received by editor(s) in revised form: March 27, 2012
Published electronically: November 5, 2013
Additional Notes: This project was partially supported by the NSF
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.