1. CMB 2015 (vol 58 pp. 281)
 Kalus, Matthias

On the Relation of Real and Complex Lie Supergroups
A complex Lie supergroup can be described as a real Lie supergroup
with integrable almost complex structure. The necessary and
sufficient conditions on an almost complex structure on a real
Lie supergroup for defining a complex Lie supergroup are deduced.
The classification of real Lie supergroups with such almost
complex
structures yields a new approach to the known classification
of complex Lie supergroups by complex HarishChandra superpairs.
A universal complexification of a real Lie supergroup is
constructed.
Keywords:Lie supergroup, almost complex structure, HarishChandra pair, universal complexification Categories:32C11, 58A50 

2. 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 $n3$. 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 structure Categories:14D20, 32C35 
