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

Lee, Y.-P.; Qu, F.

doi:10.1090/S0002-9939-2013-11800-9

Euler characteristics of universal cotangent line bundles on $\overline {\mathcal {M}}_{1,n}$
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by Y.-P. Lee and F. Qu PDF

Proc. Amer. Math. Soc. 142 (2014), 429-440 Request permission

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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