Białynicki-Birula decomposition for reductive groups

2018/05/29 by Jelisiejew, Joachim, Sienkiewicz, Łukasz · 3 citations
#14L30 #20G05 (Secondary) #20G15 (Primary) 14D22 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1805.11558

Abstract

We generalize the Białynicki-Birula decomposition from actions of G_m on smooth varieties to actions of linearly reductive group \bf G on finite type schemes and algebraic spaces. We also provide a relative version and briefly discuss the case of algebraic stacks. We define the Białynicki-Birula decomposition functorially: for a fixed \bf G-scheme X and a monoid \bf G which partially compactifies \bf G, the BB decomposition parameterizes \bf G-schemes over X for which the \bf G-action extends to the \bf G-action. The freedom of choice of \bf G makes the theory richer than the G_m-case.

Cited by

• Algebraic magnetism invariants of a double scalar action on the projective plane
• The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points
• Algebraic Magnetism

Related

• Białynicki-Birula decomposition for reductive groups in positive characteristic
• Cartan-Iwahori-Matsumoto decompositions for reductive groups
• The Chevalley-Shephard-Todd Theorem for Finite Linearly Reductive Group Schemes
• Note on the Deodhar decomposition of a double Schubert cell
• Good Representations and Homogeneous Spaces