相关论文: Cones of divisors on $\mathbb{P}^3$ blown up at ei…

We compute the facets of the effective cones of divisors on the blow-up of P^3 in up to five lines in general position. We prove that up to six lines these threefolds are weak Fano and hence Mori Dream Spaces.

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…

We compute the facets of the effective and movable cones of divisors on the blow-up of $\mathbb{P}^n$ at $n+3$ points in general position. Given any linear system of hypersurfaces of $\mathbb{P}^n$ based at $n+3$ multiple points in general…

We give a condition for certain divisors on the blow up of P^3 at points in general position to be ample. The result extends a theorem of G. Xu on the blow up of the projective plane.

In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of linear cycles, and for…

We define the Weyl cycles on $X^n_s$, the blown up projective space $\mathbb{P}^n$ in $s$ points in general position. In particular, we focus on the Mori Dream spaces $X^3_7$ and $X^{4}_{8}$, where we classify all the Weyl cycles of…

In this paper we examine the cones of effective cycles on blow ups of projective spaces along smooth rational curves. We determine explicitly the cones of divisors and 1- and 2-dimensional cycles on blow ups of rational normal curves, and…

We prove that the pseudoautomorphism group of a blow-up of $\mathbb{P}^3$ at $8$ very general points is trivial. We also establish the injectivity of the Coble representation associated to blow-ups of $\mathbb{P}^3$ at $r\ge 8$ general…

We show the existence of cones over 8-dimensional rational spheres at the boundary of the Mori cone of the blow-up of the plane at $s\geq 13$ very general points. This gives evidence for De Fernex's strong $\Delta$-conjecture, which is…

In this paper, we study the Cremona action on the nef cone of $S_n$, the blowup of $\P^2$ in $n$ very general points, with $n\ge9$. We construct and describe a rational polyhedral fundamental domain of the nef cone for $n=9$ with respect to…

A 3 dimensional analogue of Sakai's theory concerning the relation between rational surfaces and discrete Painlev\'e equations is studied. For a family of rational varieties obtained by blow-ups at 8 points in general position in ${\mathbb…

We study cones of pseudoeffective cycles on the blow up of $({\mathbb P}^1)^n$ at points in very general position, proving some results concerning their structure. In particular we show that in some cases they turn out to be generated by…

We study the birational geometry of $X^n_s$, the blow-up of $\mathbb{P}^n_\mathbb{C}$ at $s$ points in general position. We identify a set of subvarieties, which we call Weyl $r$-planes, that belong to an orbit for the action of the Weyl…

Consider the blow-up $X$ of $\mathbb{P}^3$ at 6 points in very general position and the 15 lines through the 6 points. We construct an infinite-order pseudo-automorphism $\phi_X$ on $X$, induced by the complete linear system of a divisor of…

We study divisors in the blow-up of $\mathbb{P}^n$ at points in general position that are non-special with respect to the notion of linear speciality introduced in [5]. We describe the cohomology groups of their strict transforms via the…

This article is motivated by the authors interest in the geometry of the Mori dream space $\mathbb{P}^4$ blown up in $8$ general points. In this article we develop the necessary technique for determining Weyl orbits of linear cycles for the…

In this note we consider the blowing-up X of P^3 along r general points of the anticanonical divisor of a smooth quadric in P^3. Given a complete linear system |L| = |dH - m_1 E_1 -...- m_r E_r| on X, with H the pull-back of a plane in P^3…

Nef and effective cones of divisors have been the subject of much study. In contrast, their higher codimension analogues are much harder to compute and few examples exist in the literature. In this paper we compute the nef cones in…

We study the blow-ups X of P3 along a proj. normal curve C. We look for very ample divisor classes on X of low degree, and we study the ideal of the embedding of X. Some result is generalized to higher dimensions.

In this paper we determine which blow-ups $X$ of $\mathbb{P}^n$ at general points are log Fano, that is, when there exists an effective $\mathbb{Q}$-divisor $\Delta$ such that $-(K_X+\Delta)$ is ample and the pair $(X,\Delta)$ is klt. For…