Log Fano structures and Cox rings of blow-ups of products of projective spaces

The aim of this paper is twofold. Firstly, we determine which blow-ups of products of projective spaces at general points are varieties of Fano type, and give boundary divisors making these spaces log Fano pairs. Secondly, we describe generators of the Cox rings of some cases.
Comment: 8 pages, final version, to appear in Proc. Amer. Math. Soc