scholarly journals Rank two aCM bundles on the del Pezzo threefold with Picard number 3

2015 ◽  
Vol 429 ◽  
pp. 413-446 ◽  
Author(s):  
Gianfranco Casnati ◽  
Daniele Faenzi ◽  
Francesco Malaspina
Keyword(s):  
Picard Number ◽  
Del Pezzo ◽  
Acm Bundles

scholarly journals Quotients of del Pezzo surfaces

2019 ◽  
Vol 30 (12) ◽  
pp. 1950068
Author(s):  
Andrey Trepalin
Keyword(s):  
Complete Classification ◽  
Finite Subgroup ◽  
Del Pezzo Surfaces ◽  
Picard Number ◽  
Del Pezzo Surface ◽  
Cyclic Groups ◽  
Trivial Group ◽  
Quotient Surface ◽  
Del Pezzo

Let [Formula: see text] be any field of characteristic zero, [Formula: see text] be a del Pezzo surface and [Formula: see text] be a finite subgroup in [Formula: see text]. In this paper, we study when the quotient surface [Formula: see text] can be non-rational over [Formula: see text]. Obviously, if there are no smooth [Formula: see text]-points on [Formula: see text] then it is not [Formula: see text]-rational. Therefore, under assumption that the set of smooth [Formula: see text]-points on [Formula: see text] is not empty we show that there are few possibilities for non-[Formula: see text]-rational quotients. The quotients of del Pezzo surfaces of degree [Formula: see text] and greater are considered in the author’s previous papers. In this paper, we study the quotients of del Pezzo surfaces of degree [Formula: see text]. We show that they can be non-[Formula: see text]-rational only for the trivial group or cyclic groups of order [Formula: see text], [Formula: see text] and [Formula: see text]. For the trivial group and the group of order [Formula: see text], we show that both [Formula: see text] and [Formula: see text] are not [Formula: see text]-rational if the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. For the groups of order [Formula: see text] and [Formula: see text], we construct examples of both [Formula: see text]-rational and non-[Formula: see text]-rational quotients of both [Formula: see text]-rational and non-[Formula: see text]-rational del Pezzo surfaces of degree [Formula: see text] such that the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. As a result of complete classification of non-[Formula: see text]-rational quotients of del Pezzo surfaces we classify surfaces that are birationally equivalent to quotients of [Formula: see text]-rational surfaces, and obtain some corollaries concerning fields of invariants of [Formula: see text].

scholarly journals Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section

2018 ◽  
Vol 222 (3) ◽  
pp. 585-609 ◽  
Author(s):  
Gianfranco Casnati ◽  
Daniele Faenzi ◽  
Francesco Malaspina
Keyword(s):  
Hyperplane Section ◽  
Del Pezzo ◽  
Acm Bundles

scholarly journals BOUNDING THE VOLUMES OF SINGULAR WEAK LOG DEL PEZZO SURFACES

2013 ◽  
Vol 24 (13) ◽  
pp. 1350110 ◽  
Author(s):  
CHEN JIANG
Keyword(s):  
Upper Bound ◽  
General Position ◽  
Del Pezzo Surfaces ◽  
Minimal Resolution ◽  
Picard Number ◽  
Hirzebruch Surface ◽  
Del Pezzo Surface ◽  
Blowing Up ◽  
Del Pezzo ◽  
Log Del Pezzo Surfaces

We give an optimal upper bound for the anti-canonical volume of an ϵ-lc weak log del Pezzo surface. Moreover, we consider the relation between the bound of the volume and the Picard number of the minimal resolution of the surface. Furthermore, we consider blowing up several points on a Hirzebruch surface in general position and give some examples of smooth weak log del Pezzo surfaces.

scholarly journals On Cox rings of K3 surfaces

2010 ◽  
Vol 146 (4) ◽  
pp. 964-998 ◽  
Author(s):  
Michela Artebani ◽  
Jürgen Hausen ◽  
Antonio Laface
Keyword(s):  
K3 Surfaces ◽  
Del Pezzo Surfaces ◽  
K3 Surface ◽  
Picard Number ◽  
Finitely Generated ◽  
Generators And Relations ◽  
Cox Rings ◽  
Double Covers ◽  
Del Pezzo ◽  
Effective Cone

AbstractWe study Cox rings of K3 surfaces. A first result is that a K3 surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3 surfaces of Picard number two, and explicitly compute the Cox rings of generic K3 surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.

scholarly journals Codimension one Fano distributions on Fano manifolds

2018 ◽  
Vol 20 (05) ◽  
pp. 1750058 ◽  
Author(s):  
Carolina Araujo ◽  
Mauricio Corrêa ◽  
Alex Massarenti
Keyword(s):  
Moduli Spaces ◽  
Projective Spaces ◽  
Complete Intersections ◽  
Picard Number ◽  
Contact Manifolds ◽  
Fano Manifolds ◽  
Codimension One ◽  
Linear Sections ◽  
Del Pezzo

In this paper, we investigate codimension one Fano distributions on Fano manifolds with Picard number one. We classify Fano distributions of maximal index on complete intersections in weighted projective spaces, Fano contact manifolds, Grassmannians of lines and their linear sections, and describe their moduli spaces. As a consequence, we obtain a classification of codimension one del Pezzo distributions on Fano manifolds with Picard number one.

scholarly journals Rank two aCM bundles on the del Pezzo threefold of degree 7

2016 ◽  
Vol 30 (1) ◽  
pp. 129-165 ◽  
Author(s):  
Gianfranco Casnati ◽  
Matej Filip ◽  
Francesco Malaspina
Keyword(s):  
Del Pezzo ◽  
Acm Bundles

Examples of K-Unstable Fano Manifolds with the Picard Number 1

2017 ◽  
Vol 60 (4) ◽  
pp. 881-891 ◽  
Author(s):  
Kento Fujita
Keyword(s):  
Picard Number ◽  
Fano Manifolds ◽  
Del Pezzo

AbstractWe show that the pair (X, –KX) is K-unstable for a del Pezzo manifold X of degree 5 with dimension 4 or 5. This disproves a conjecture of Odaka and Okada.

scholarly journals Affine cones over cubic surfaces are flexible in codimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Perepechko
Keyword(s):  
Automorphism Group ◽  
Open Subset ◽  
Pezzo Surface ◽  
Ample Divisor ◽  
Transitive Action ◽  
Del Pezzo Surface ◽  
Codimension One ◽  
Cubic Surfaces ◽  
Special Automorphism ◽  
Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

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