Related papers: Del Pezzo surfaces with four log terminal singular…
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 classify equivariantly Gorenstein log del Pezzo surfaces with boundaries at infinity and with finite group actions such that the quotient surface modulo the finite group has Picard number one. We also determine the corresponding finite…
We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.
In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type…
We study global log canonical thresholds of del Pezzo surfaces.
We present efficient classification algorithms for log del Pezzo surfaces with torus action of Picard number one and given Gorenstein index. Explicit results are obtained up to Gorenstein index 200.
We study del Pezzo fibrations of degree 1 with terminal singularities. A connection between singularities on del Pezzo surfaces of degree 1 and Kodaira's classification of elliptic singular fibers will be studied in this paper. By this…
We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is 1/k-log canonical if it allows a resolution of singularities with discrepanies all greater or equal to 1/k-1. We provide a concrete classification…
We classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger than one.
We complete the classification of automorphism groups of del Pezzo surfaces over algebraically closed fields of odd positive characteristic.
Sur toute surface de del Pezzo de degr\'e 4 sur un corps $C_1$ de caract\'eristique z\'ero, tous les points rationnels sont R-\'equivalents. Plus g\'en\'eralement, ceci vaut sur tout corps parfait infini de caract\'eristique diff\'erente de…
In this article, we consider weak del Pezzo surfaces defined over a finite field, and their associated, singular, anticanonical models. We first define arithmetic types for such surfaces, by considering the Frobenius actions on their Picard…
The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not…
We compute the complexity of del Pezzo surfaces with du Val singularities.
Hirschfeld classified split del Pezzo surfaces of degree at least three whose points are all contained on the lines in the surface. We continue his work and begin the classification of split degree two del Pezzo surfaces over finite fields…
We prove that a terminal three-dimensional del Pezzo fibration has no fibers of multiplicity $\ge 6$. We also obtain a rough classification possible configurations of singular points on multiple fibers and give some examples.
We find normal forms for del Pezzo surfaces of degree $2$ over algebraically closed fields of characteristic $2$. For each normal form, we describe the structure of the group of automorphisms of the surface. In particular, we classify all…
Let k be a perfect field. Recently J.-L. Colliot-Th\'el\`ene showed that two pointless quadric surfaces over k are birationally equivalent if and only if they are isomorphic. We show that this result holds for arbitrary del Pezzo surfaces…
We address the question of the degree of unirational parameterizations of degree four and degree three del Pezzo surfaces. Specifically we show that degree four del Pezzo surfaces over finite fields admit degree two parameterizations and…
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.