location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword complex structure

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2002 (vol 45 pp. 417)

Kamiyama, Yasuhiko; Tsukuda, Shuichi
 On Deformations of the Complex Structure on the Moduli Space of Spatial Polygons For an integer \$n \geq 3\$, let \$M_n\$ be the moduli space of spatial polygons with \$n\$ edges. We consider the case of odd \$n\$. Then \$M_n\$ is a Fano manifold of complex dimension \$n-3\$. Let \$\Theta_{M_n}\$ be the sheaf of germs of holomorphic sections of the tangent bundle \$TM_n\$. In this paper, we prove \$H^q (M_n,\Theta_{M_n})=0\$ for all \$q \geq 0\$ and all odd \$n\$. In particular, we see that the moduli space of deformations of the complex structure on \$M_n\$ consists of a point. Thus the complex structure on \$M_n\$ is locally rigid. Keywords:polygon space, complex structureCategories:14D20, 32C35