arXiv subjects
Publications and source records attributed to Keisuke Miyamoto.
We can run the MMP for any divisor on any $\mathbb{Q}$-factorial projective toric variety. We show that two Mori fiber spaces, which are outputs of the above MMP, are connected by finitely many elementary transforms.
We show that the Nakai--Moishezon ampleness criterion holds for real line bundles on complete schemes. As applications, we treat the relative Nakai--Moishezon ampleness criterion for real line bundles and the Nakai--Moishezon ampleness criterion for real line bundles on complete algebraic spaces. The main ingredient of this paper is Birkar's characterization of augmented base loci of real divisors on projective schemes.
We give a characterization of projective spaces for quasi-log canonical pairs from the Mori theoretic viewpoint.
We show that the Sarkisov program holds for $\mathbb{Q}$-factorial log surfaces and log canonical surfaces over any algebraically closed field.