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June 2001 Sheaf Cohomology of the Moduli Space of Spatial Polygons and Lattice Points
Yasuhiko KAMIYAMA
Tokyo J. Math. 24(1): 205-209 (June 2001). DOI: 10.3836/tjm/1255958324

Abstract

Let $\mathcal{M}_n$ be the moduli space of spatial polygons with $n$ edges. We consider the case of odd $n$. Let $K_{n}^{*}=\Lambda^{n-3}T\mathcal{M}_n$ be the dual bundle of the canonical bundle on $\mathcal{M}_n$. In this paper we determine the sheaf cohomology $H^*(\mathcal{M}_n,K_{n}^{*})$. We have $H^q(\mathcal{M}_n,K_{n}^{*})=0$ $(q\geq 1)$ and $\dim H^0(\mathcal{M}_n,K_{n}^{*})$ is equal to the number of lattice points in the convex polytope $\Delta_n$ in $\mathbf{R}^{n-3}$.

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Yasuhiko KAMIYAMA. "Sheaf Cohomology of the Moduli Space of Spatial Polygons and Lattice Points." Tokyo J. Math. 24 (1) 205 - 209, June 2001. https://doi.org/10.3836/tjm/1255958324

Information

Published: June 2001
First available in Project Euclid: 19 October 2009

zbMATH: 1037.53057
MathSciNet: MR1844430
Digital Object Identifier: 10.3836/tjm/1255958324

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

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Vol.24 • No. 1 • June 2001
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