Log canonical thresholds on group compactifications
Thibaut Delcroix (IF)

TL;DR
This paper calculates the log canonical thresholds for certain line bundles on group compactifications, linking geometric properties to convex functions and polytopes, and providing a formula for the alpha invariant.
Contribution
It introduces a method to compute log canonical thresholds using convex functions and polytopes, advancing understanding of singular hermitian metrics on group compactifications.
Findings
Derived a formula for log canonical thresholds in terms of convex functions.
Connected asymptotic behavior of convex functions to thresholds.
Provided a new expression for the alpha invariant based on polytopes.
Abstract
We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex reductive groups. To this end, we associate to any such metric a convex function whose asymptotic behavior determines the log canonical threshold. As a consequence we obtain a formula for the alpha invariant of these line bundles, in terms of the polytope associated to the group compactification.
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.
