Examples and Counterexamples for Existence of Categorical Quotients
A. A'Campo-Neuen, J. Hausen
TL;DR
This paper explores when categorical quotients exist or do not exist for algebraic group actions, focusing on subtorus actions on toric varieties, providing illustrative examples in algebraic geometry.
Contribution
It presents new examples demonstrating both existence and non-existence of categorical quotients in the context of toric varieties and algebraic group actions.
Findings
Examples of subtorus actions with categorical quotients
Examples of subtorus actions without categorical quotients
Insights into conditions affecting quotient existence
Abstract
We give examples for existence and non-existence of categorical quotients for algebraic group actions in the categories of algebraic varieties and prevarieties. All our examples are subtorus actions on toric varieties.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Rings, Modules, and Algebras · Advanced Algebra and Geometry