Alpha-invariant of Toric Line Bundles

Thibaut Delcroix (1)

1 IF - Institut Fourier

We generalize the work of Jian Song to compute the alpha invariant of any (nef and big) toric line bundle in terms of the associated polytope. We use the analytic version of the computation of the log canonical threshold of monomial ideals to give the log canonical threshold of any non-negatively curved singular hermitian metric on the line bundle, and deduce the alpha invariant from this.

Mots clés: log canonical threshold; alpha invariant; toric; polytope

Domaines: Géométrie algébrique [math.AG]

Thibaut Delcroix. Alpha-invariant of Toric Line Bundles. Annales Polonici Mathematici, 2015, 114, pp.13-27. ⟨10.4064/ap114-1-2⟩. ⟨hal-01059943v2⟩