On the body of ample angles of asymptotically log Fano varieties

Abstract

In dimension two, we reduce the classification problem for asymptotically log Fano pairs to the problem of determining generality conditions on certain blow-ups. In any dimension, we prove the rationality of the body of ample angles of an asymptotically log Fano pair, i.e., these convex bodies are always rational polytopes.

v2: Theorem 1.4 has been improved and now completely settles Problem 1.3; v3: final version to appear in Rendiconti del Circolo Matematico di Palermo

References in corpus (2)

• Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces
• High-dimensional convex sets arising in algebraic geometry