2011/01/20 by Rudolf Tange, Tange, Rudolf · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1101.3938
openalex publication_date 2011/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mc G be a reductive group over an algebraically closed field of characteristic p>0. We study homogeneous \mc G-spaces that are induced from the G× G-space G, G a suitable reductive group, along a parabolic subgroup of \mc G. We show that, under certain mild assumptions, any (normal) equivariant embedding of such a homogeneous space is canonically Frobenius split compatible with certain subvarieties and has an equivariant rational resolution by a toroidal embedding. In particular, all these embeddings are Cohen-Macaulay. Examples are the G× G-orbits in normal reductive monoids with unit group G. Our class of homogeneous spaces also includes the open orbits of the well-known determinantal varieties and the varieties of (circular) complexes. We also show that all G-orbit closures in a spherical variety which is canonically Frobenius split are normal. Finally we study the Gorenstein property for the varieties of circular complexes and for a related reductive monoid.