Sheaf Cohomology of the Moduli Space of Spatial Polygons and Lattice Points

KAMIYAMA, Yasuhiko

Tokyo J. of Math., Tome 24 (2001) no. 2, p. 205-209 / Harvested from Project Euclid

Résumé

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 $\mathbf{R}^{n-3}$.

Publié le : 2001-06-15
Classification:

@article{1255958324,
     author = {KAMIYAMA, Yasuhiko},
     title = {Sheaf Cohomology of the Moduli Space of Spatial Polygons and Lattice Points},
     journal = {Tokyo J. of Math.},
     volume = {24},
     number = {2},
     year = {2001},
     pages = { 205-209},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958324}
}

KAMIYAMA, Yasuhiko. Sheaf Cohomology of the Moduli Space of Spatial Polygons and Lattice Points. Tokyo J. of Math., Tome 24 (2001) no. 2, pp.  205-209. http://gdmltest.u-ga.fr/item/1255958324/