2017/07/20 by Weingart, Gregor
#53C30 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.06385
Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local geometry of an affine homogeneous space we construct an algebraic variety \mathfrakM(\mathfrakgl V), which serves as a coarse moduli space for the local isometry classes of affine homogeneous spaces of dimension dim V. Moreover we associate a SymV^*-comodule to a point in \mathfrakM(\mathfrakgl V ) and use its Spencer cohomology in order to describes the infinitesimal deformations of this point in the true moduli space \mathfrakM_∞(\mathfrakgl V ).