Sheaf cohomology of the moduli space of spatial polygons and lattice points. (Q5946904)

The author studies the moduli space of polygons with \(n\) edges in \(\mathbb{R}^3\), where \(n\) is odd and bigger or equal than \(5\) (when \(n= 3\) the moduli space reduces simply to a point). Two such polygons are identified if they differ only by motions in \(\mathbb{R}^3\). In this situation, the moduli space is a Fano manifold of dimension \(n- 3\). The main result of the paper is on the cohomology of the anti-canonical sheaf of the moduli space. The author shows that the \(q\)th cohomology vanishes for \(q\geq 1\) and gives a very explicit formula for the dimension of the \(0\)th cohomology.