On the anticanonical complex
Christoff Hische, Milena Wrobel

TL;DR
This paper extends the concept of the anticanonical complex from toric Fano varieties to higher complexity torus actions, enabling new classifications of three-dimensional canonical Fano varieties with specific automorphism groups.
Contribution
It generalizes the anticanonical complex to higher complexity varieties and applies this to classify certain three-dimensional Fano varieties.
Findings
Extended the anticanonical complex to higher complexity varieties
Classified three-dimensional canonical Fano intrinsic quadrics with specific automorphism groups
Demonstrated the utility of the generalized complex in variety classification
Abstract
The anticanonical complex has been introduced as a natural generalization of the toric Fano polytope and so far has been succesfully used for the study of varieties with a torus action of complexity one. In the present article we enlarge the area of application of the anticanonical complex to varieties with a torus action of higher complexity, for example, general arrangement varieties. As an application of our techniques we classify the three-dimensional canonical Fano intrinsic quadrics with automorphism group having a maximal torus of dimension one.
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 · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
