Log Fano blowups of mixed products of projective spaces and their effective cones

Abstract

We compute the cones of effective divisors on blowups of ${\mathbb{P}}^1\times {\mathbb{P}}^2$ and ${\mathbb{P}}^1\times {\mathbb{P}}^3$ in up to 6 points. We also show that all these varieties are log Fano, giving a conceptual explanation for the fact that all the cones we compute are rational polyhedral.

arXiv comment49 pages + ancillary Normaliz files; v2: added Lemma 3.12 and corrected the statement of Theorem 3.16. Accepted for publication in Rev. Mat. Complut