Compactifications of configuration spaces of homogeneous spaces

• Applicant: Privatdozent Dr. Markus Perling
• Subject Area: Mathematics
• Term: from 2004 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5440686

The aim of this project is to study configuration spaces of flag varieties in algebraic geometry. Here, by a flag variety we mean a homogeneous space of the form G/P, where G is a connected linear algebraic group and P is a parabolic subgroup, where in particular we focus on Grassmannians and varieties of full flags. The configuration spaces we are interested in are spaces parametrizing configurations of n points in the spaces G/P, up to global automorphisms by G. In order to obtain such configuration spaces as good quotients in the sense of geometric invariant theory, we want to investigate the combinatorics of the stratification induced by the diagonal action of G. Our starting point is earlier work by Gelfand and MacPherson, where configurations of points in projective spaces were combinatorically classified using the language of matriods. By unsing recent generalizations of Lafforgue, we want to extend this classification to the case of configurations of points in Grassmannians and flag varieties. The resulting stratification of the n-fold product of G/P will allow an explicit combinatorial determination of the G-orbits in this space. Using this we will investigate constructions of good quotients which are compact spaces and whose geometry allows an explicit combinatorial description.

• DFG Programme: Research Fellowships
• International Connection: France
• Cooperation Partner: Professor Dr. Michel Brion