相关论文: On del Pezzo fibrations in positive characteristic

We classify the automorphism groups of del Pezzo surfaces of degrees one and two over an algebraically closed field of characteristic two. This finishes the classification of automorphism groups of del Pezzo surfaces in all characteristics.

We characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type $\mathbf{A}_3$ over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these…

In this paper we give an upper bound for the Picard number of the rational surfaces which resolve minimally the singularities of toric log Del Pezzo surfaces of given index $\ell$. This upper bound turns out to be a quadratic polynomial in…

In this paper we give a criterion for birational rigidity of del Pezzo fibrations of degree 1 and 2 with only quotient singularities. As an application, we prove birational rigidity of suitable del Pezzo fibrations admitting an action of…

We prove orientation results for evaluation maps of moduli spaces of rational stable maps to del Pezzo surfaces over a field, both in characteristic $0$ and in positive characteristic. These results and the theory of degree developed in a…

Toric log del Pezzo surfaces correspond to convex lattice polygons containing the origin in their interior and having only primitive vertices. An upper bound on the volume and on the number of boundary lattice points of these polygons is…

We investigate the possible self-intersection numbers for sections of surface bundles and Lefschetz fibrations over surfaces. When the fiber genus g and the base genus h are positive, we prove that the adjunction bound 2h-2 is the only…

We show that simultaneous log resolutions of simply elliptic singularities can be constructed inside suitable stacks of principal bundles over elliptic curves. In particular, we give a direct geometrical construction of del Pezzo surfaces…

Del Pezzo surfaces over C with log terminal singularities of index \le 2 were classified by Alekseev and Nikulin. In this paper, for each of these surfaces, we find an appropriate morphism to projective space. These morphisms enable us to…

I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q>0. Such things can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo…

In this article, we give the classification of normal del Pezzo surfaces of rank one with at most log canonical singularities containing the affine plane defined over an algebraically non-closed field of characteristic zero. As an…

The surfaces considered are real, rational and have a unique smooth real $(-2)$-curve. Their canonical class $K$ is strictly negative on any other irreducible curve in the surface and $K^2>0$. For surfaces satisfying these assumptions, we…

This is a report of the author's talk at Algebra Symposium 2019 held at Tohoku University. We discuss some improvements of Mori's Bend and Break for sections of del Pezzo fibrations over $\mathbb P^1$.

We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that…

Varieties fibered into del Pezzo surfaces form a class of possible outputs of the minimal model program. It is known that del Pezzo fibrations of degrees $1$ and $2$ over the projective line with smooth total space satisfying the so-called…

We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with non-zero signature.…

This is the first article in a series aimed at classifying normal del Pezzo surfaces of Picard rank one over algebraically closed fields of arbitrary characteristic up to an isomorphism. Our guiding invariant is the height of a del Pezzo…

We find a characterization for Fano 4-folds $X$ with Lefschetz defect $\delta_{X}=3$: besides the product of two del Pezzo surfaces, they correspond to varieties admitting a conic bundle structure $f\colon X\to Y$ with…

In this article, we use a correspondence between Ulrich bundles on a projective variety and quiver representations to prove that certain del Pezzo surfaces satisfy the Ulrich trichotomy, for any given polarization.

We determine the tropicalizations of very affine surfaces over a valued field that are obtained from del Pezzo surfaces of degree 5, 4 and 3 by removing their (-1)-curves. On these tropical surfaces, the boundary divisors are represented by…