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Related papers: Del Pezzo surfaces with many symmetries

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For split smooth Del Pezzo surfaces, we analyse the structure of the effective cone and prove a recursive formula for the value of alpha, appearing in the leading constant as predicted by Peyre of Manin's conjecture on the number of…

Number Theory · Mathematics 2007-05-23 Ulrich Derenthal

We prove that $\delta$-invariants of smooth cubic surfaces are at least $\frac{6}{5}$.

Algebraic Geometry · Mathematics 2019-07-15 Ivan Cheltsov , Kewei Zhang

We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.

alg-geom · Mathematics 2008-02-03 N. Mohan Kumar

We construct the first examples of regular del Pezzo surfaces for which the irregularity (i.e. the dimension of the first cohomology group of the structure sheaf) is nonzero. We also find a restriction on the integer pairs that are possible…

Algebraic Geometry · Mathematics 2013-04-23 Zachary Maddock

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…

Algebraic Geometry · Mathematics 2025-08-20 Karol Palka , Tomasz Pełka

In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 1.

Algebraic Geometry · Mathematics 2025-08-26 Elena Denisova

We study del Pezzo varieties, higher-dimensional analogues of del Pezzo surfaces. In particular, we introduce ADE classification of del Pezzo varieties, show that in type A the dimension of non-conical del Pezzo varieties is bounded by $12…

Algebraic Geometry · Mathematics 2022-10-14 Alexander Kuznetsov , Yuri Prokhorov

We show that smooth quintic del Pezzo threefolds over arbitrary base schemes are classified by non-degenerate ternary symmetric bilinear forms. Then we describe the automorphism group schemes, the Hilbert schemes of lines and the orbit…

Algebraic Geometry · Mathematics 2025-11-20 Tetsushi Ito , Akihiro Kanemitsu , Teppei Takamatsu , Yuuji Tanaka

In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree $\ge 4$.

Algebraic Geometry · Mathematics 2025-08-26 Elena Denisova

We classify codimension 2 well-formed and quasi-smooth weighted complete intersection del Pezzo surfaces.

Algebraic Geometry · Mathematics 2016-08-09 Evgeny Mayanskiy

We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.

Algebraic Geometry · Mathematics 2020-11-10 In-kyun Kim , Joonyeong Won

We give an explicit counter-example to a conjecture of Kyusik Hong and Joonyeong Won about $\alpha$-invariants of polarized smooth del Pezzo surfaces of degree one.

Algebraic Geometry · Mathematics 2016-11-07 Ivan Cheltsov

In this article, we compute $\delta$-invariant of Du Val del Pezzo surfaces of degree $3$.

Algebraic Geometry · Mathematics 2025-08-26 Elena Denisova

We compute the coregularity of del Pezzo surfaces with du Val singularities. To this aim, we study the relation between del Pezzo surfaces of degree $1$ and elliptic fibrations. It turns out that del Pezzo surfaces with positive…

Algebraic Geometry · Mathematics 2026-03-04 Konstantin Loginov , Andrey Trepalin

We classify del Pezzo surfaces with Picard number is equal to one and with four log terminal singular points.

Algebraic Geometry · Mathematics 2025-12-24 Grigory Belousov , DongSeon Hwang

We determine which singular del Pezzo surfaces are equivariant compactifications of G_a^2, to assist with proofs of Manin's conjecture for such surfaces. Additionally, we give an example of a singular quartic del Pezzo surface that is an…

Algebraic Geometry · Mathematics 2010-03-15 Ulrich Derenthal , Daniel Loughran

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model…

Algebraic Geometry · Mathematics 2015-10-07 Alessio Corti , Liana Heuberger

This paper focuses on the classification of all toric log Del Pezzo surfaces with exactly one singularity up to isomorphism, and on the description of how they are embedded as intersections of finitely many quadrics into suitable projective…

Algebraic Geometry · Mathematics 2017-06-13 Dimitrios I. Dais

We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration…

Algebraic Geometry · Mathematics 2025-11-12 Fabio Bernasconi , Hiromu Tanaka

In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 2.

Algebraic Geometry · Mathematics 2025-08-26 Elena Denisova