Log canonical thresholds on group compactifications

Thibaut Delcroix (1)

1 IF - Institut Fourier

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.

Mots clés: Log canonical threshold; alpha invariant; group compactification; polytope

Domaines: Géométrie algébrique [math.AG]; Géométrie différentielle [math.DG]

Thibaut Delcroix. Log canonical thresholds on group compactifications. 2015. ⟨hal-01216641v1⟩