Cox rings are significant global invariants of algebraic varieties, naturally generalizing
homogeneous coordinate rings of projective spaces. This book provides a largely self …

But, in the further development of a branch of mathematics, the human mind, encouraged by
the success of its solutions, becomes conscious of its independence. It evolves from itself …

Bs (mD), where Bs (mD) denotes the base locus of the linear system| mD|. This is an
interesting and basic invariant, but well-known pathologies associated to linear series have …

We classify all generalized del Pezzo surfaces (that is, minimal desingularizations of
singular del Pezzo surfaces containing only rational double points) whose universal torsors …

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal
for us is to understand the cohomology of" quotients" under such actions, by generalizing …

We degenerate Cox–Nagata rings to toric algebras by means of sagbi bases induced by
configurations over the rational function field. For del Pezzo surfaces, this degeneration …

Abstract We prove the Morrison-Kawamata cone conjecture for Kawamata log terminal
Calabi-Yau pairs in dimension 2. For a large class of rational surfaces as well as for K3 …

In this paper we study the cones of higher codimension (pseudo) effective cycles on point
blowups of projective space. We determine bounds on the number of points for which these …

We prove that the Cox ring of the moduli space $\overline {M} _ {0, 6} $, of stable rational
curves with $6 $ marked points, is finitely generated by sections corresponding to the …

Explicit log Fano structures on blow-ups of projective spaces | Proceedings of the London
Mathematical Society | Oxford Academic Skip to Main Content Advertisement Oxford …