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.

Classification of strongly asymptotically log del Pezzo flags and surfaces

“…In §3 we show any strongly asymptotically log del Pezzo pair can be described as a proper blow-up of another strongly asymptotically log del Pezzo pair with a smaller Picard group. The key result here is Proposition 3.3 which is more conceptual approach than that given in [2] and which generalizes to the setting of asymptotically log del Pezzo pairs [1]. In §5 we turn to the main application, the classification of strongly asymptotically log del Pezzo pairs (Theorem 5.1).…”

“…], [0,(2,2)], [0,(2,1), (0, 1)], [0,(2,1)] . (6.5) When max i a i = 1, we split into two subcases: when there are at least two pairs (a i , b i ) with all coefficients positive: [n, (a 1 , b 1 ), .…”

“…(2,3)] = (I.5B.1),[1, (2, 2), (0, 1)] = (II.5A.1) (a),[1, (2, 2)] = (I.3A), [0,(2,2)] = (I.4A), [0,(2,1), (0, 1)] = (II.4B), [0, (2, 1)] = (I.4B).In(6.6) [2,(1,2),(1,2)] is excluded as Z 2 . (Z 2 + 2F ) = Z 2 .…”