Abstract
We generalize the Białynicki-Birula decomposition from actions of Gm on smooth varieties to actions of a linearly reductive group 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 G-scheme X and a monoid G‾ which partially compactifies G, the BB decomposition parameterizes G-schemes over X for which the G-action extends to the G‾-action. The freedom of choice of G‾ makes the theory richer than the Gm-case.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
