We construct projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone. As a consequence, we prove that the pseudo-effective cone of the Grothendieck–Knudsen moduli space \bar{M_{0,n} of stable rational curves is not polyhedral for n >= 10. These results hold both in characteristic 0 and in characteristic p, for all primes p. Many of these toric surfaces are related to an interesting class of arithmetic threefolds that we call arithmetic elliptic pairs of infinite order. Our analysis relies on tools of arithmetic geometry and Galois representations in the spirit of the Lang–Trotter conjecture, producing toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone...
We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely gen...
© 2018 International Press of Boston, Inc.. All rights reserved. We prove that, for a K3 surface in ...
While the Chow groups of 0-dimensional cycles on the moduli spaces of Deligne-Mumford stable pointed...
An elliptic pair $(X, C)$ is a projective rational surface $X$ with log terminal singularities, and ...
A central problem of modern minimal model theory is to describe the various cones of divisors associ...
The cycles on an algebraic variety contain a great deal of information about its geometry. This thes...
AbstractWe give a numerical criterion for ensuring the finite generation of the effective monoid of ...
24 pagesInternational audienceWe describe the positive cone and the pseudo-effective cone of a non-K...
Normal projective surfaces admitting non-isomorphic surjective endomorphisms are classified up to is...
We compute the facets of the effective and movable cones of divisors on the blow-up of Pn at n + 3 p...
We compute the facets of the effective and movable cones of divisors on the blow-up of P^n at n+3 po...
ABSTRACT. We give a conjectural description for the cone of effective divisors of the Grothendieck–K...
The families of smooth rational surfaces in P"4 have been classified in degree #<=# 10. All ...
We discuss a couple of problems concerning the pseudoeffective cone of a projective variety. In the ...
In this paper, we study effective, nef and semiample cones of surfaces isogenous to a product of mix...
We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely gen...
© 2018 International Press of Boston, Inc.. All rights reserved. We prove that, for a K3 surface in ...
While the Chow groups of 0-dimensional cycles on the moduli spaces of Deligne-Mumford stable pointed...
An elliptic pair $(X, C)$ is a projective rational surface $X$ with log terminal singularities, and ...
A central problem of modern minimal model theory is to describe the various cones of divisors associ...
The cycles on an algebraic variety contain a great deal of information about its geometry. This thes...
AbstractWe give a numerical criterion for ensuring the finite generation of the effective monoid of ...
24 pagesInternational audienceWe describe the positive cone and the pseudo-effective cone of a non-K...
Normal projective surfaces admitting non-isomorphic surjective endomorphisms are classified up to is...
We compute the facets of the effective and movable cones of divisors on the blow-up of Pn at n + 3 p...
We compute the facets of the effective and movable cones of divisors on the blow-up of P^n at n+3 po...
ABSTRACT. We give a conjectural description for the cone of effective divisors of the Grothendieck–K...
The families of smooth rational surfaces in P"4 have been classified in degree #<=# 10. All ...
We discuss a couple of problems concerning the pseudoeffective cone of a projective variety. In the ...
In this paper, we study effective, nef and semiample cones of surfaces isogenous to a product of mix...
We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely gen...
© 2018 International Press of Boston, Inc.. All rights reserved. We prove that, for a K3 surface in ...
While the Chow groups of 0-dimensional cycles on the moduli spaces of Deligne-Mumford stable pointed...