Related papers: Classification of Canonical Del Pezzo Orders
We construct two types of wellformed and quasismooth biregular models (infinite series) of rigid orbifold del Pezzo surfaces having their (sub) anti-canonical embeddings in $\mathbb P^6(w_i) $. One type of model contains a family of rigid…
In our preprint: "Algebraic surfaces with log-terminal singularities and nef anticanonical class and reflection groups in Lobachevsky spaces", Preprint Max-Planck-Institut f\"ur Mathematik, Bonn, (1989) MPI/89-28 (Russian), we had extended…
In this note, we construct some minimal smooth surfaces of general type with canonical map of degree $ 13, 15, 17, 18, 21, 22 $. These surfaces are constructed as $ \mathbb{Z}_{3}^2$-covers of a blow-up of $ \mathbb{P}^1 \times \mathbb{P}^1…
For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.
In this article we classify quadruple Galois canonical covers of smooth surfaces of minimal degree. The classification shows that they are either non-simple cyclic covers or bi-double covers. If they are bi-double then they are all fiber…
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
In this paper we study quotients of del Pezzo surfaces of degree four and more over arbitrary field $\Bbbk$ of characteristic zero by finite groups of automorphisms. We show that if a del Pezzo surface $X$ contains a point defined over the…
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…
Marginally trapped surfaces are spacelike surfaces in the Minkowski space whose mean curvature vector is lightlike at each point. In general, the marginally trapped surfaces are determined by seven functions satisfying several conditions…
We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold K\"ahler--Einstein metrics…
It is well-known that del Pezzo surfaces of degree $9-n$ one-to-one correspond to flat $E_n$ bundles over an elliptic curve. In this paper, we construct $ADE$ bundles over a broader class of rational surfaces which we call $ADE$ surfaces,…
Totally real surfaces in the nearly K\"ahler $\mathbb{C}P^3$ are investigated and are completely classified under various additional assumptions, resulting in multiple new examples. Among others, the classification includes totally real…
In this paper we continue the study of algebraic fundamentale group of minimal surfaces of general type S satisfying K_S^2<3\chi(S). We show that, if K_S^2= 3\chi(S)-1 and the algebraic fundamental group of S has order 8, then S is a…
Inspired by the recent progress by Coates-Corti-Kasprzyk et al. on Mirror Symmetry for del Pezzo surfaces, we show that for any positive integer k the deformation families of del Pezzo surfaces with a single 1/k(1,1) singularity (and no…
We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that…
The "canonical dimension" of an algebraic group over a field by definition is the maximum of the canonical dimensions of principal homogenous spaces under that group. Over a field of characteristic zero, we prove that the canonical…
We address weak approximation for certain del Pezzo surfaces defined over the function field of a curve. We study the rational connectivity of the smooth locus of degree two del Pezzo surfaces with two A1 singularities in order to prove…
On del Pezzo surfaces, we study effective ample $\mathbb{R}$-divisors such that the complements of their supports are isomorphic to $\mathbb{A}^1$-bundles over smooth affine curves.
We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ to the case of Del Pezzo surfaces of degree 1, where we explicitly…
It is known that a given smooth del Pezzo surface or Fano threefold $X$ admits a choice of log Calabi-Yau compactified mirror toric Landau-Ginzburg model (with respect to certain fixed K\"ahler classes and Gorenstein toric degenerations).…