scholarly journals On pliability of del Pezzo fibrations and Cox rings

2017 ◽  
Vol 2017 (723) ◽  
Author(s):  
Hamid Ahmadinezhad
Keyword(s):  
Moduli Space ◽  
Toric Varieties ◽  
Projective Spaces ◽  
Low Rank ◽  
Del Pezzo Surfaces ◽  
Coordinate Ring ◽  
Birational Transformations ◽  
Cox Rings ◽  
Del Pezzo

AbstractWe develop some concrete methods to build Sarkisov links, starting from Mori fibre spaces. This is done by studying low rank Cox rings and their properties. As part of this development, we give an algorithm to construct explicitly the coarse moduli space of a toric Deligne–Mumford stack. This can be viewed as the generalisation of the notion of well-formedness for weighted projective spaces to homogeneous coordinate ring of toric varieties. As an illustration, we apply these methods to study birational transformations of certain fibrations of del Pezzo surfaces over

scholarly journals Cox rings of degree one del Pezzo surfaces

2009 ◽  
Vol 3 (7) ◽  
pp. 729-761 ◽  
Author(s):  
Damiano Testa ◽  
Anthony Várilly-Alvarado ◽  
Mauricio Velasco
Keyword(s):  
Del Pezzo Surfaces ◽  
Cox Rings ◽  
Del Pezzo

scholarly journals Del Pezzo Surfaces in Weighted Projective Spaces

2018 ◽  
Vol 61 (2) ◽  
pp. 545-572
Author(s):  
Erik Paemurru
Keyword(s):  
Projective Spaces ◽  
Del Pezzo Surfaces ◽  
Del Pezzo

AbstractWe study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm to classify all of them.

scholarly journals Hilbert functions of Cox rings of del Pezzo surfaces

2017 ◽  
Vol 480 ◽  
pp. 309-331
Author(s):  
Jinhyung Park ◽  
Joonyeong Won
Keyword(s):  
Hilbert Functions ◽  
Del Pezzo Surfaces ◽  
Cox Rings ◽  
Del Pezzo

scholarly journals Gröbner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces

2007 ◽  
Vol 316 (2) ◽  
pp. 777-801 ◽  
Author(s):  
Mike Stillman ◽  
Damiano Testa ◽  
Mauricio Velasco
Keyword(s):  
Gröbner Bases ◽  
Group Actions ◽  
Grobner Bases ◽  
Del Pezzo Surfaces ◽  
Cox Rings ◽  
Monomial Group ◽  
Del Pezzo

scholarly journals Derived categories of quintic del Pezzo fibrations

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Fei Xie
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Derived Categories ◽  
Derived Category ◽  
The Other ◽  
Del Pezzo Surfaces ◽  
Linear Section ◽  
Projective Duality ◽  
Del Pezzo ◽  
Space Approach

AbstractWe provide a semiorthogonal decomposition for the derived category of fibrations of quintic del Pezzo surfaces with rational Gorenstein singularities. There are three components, two of which are equivalent to the derived categories of the base and the remaining non-trivial component is equivalent to the derived category of a flat and finite of degree 5 scheme over the base. We introduce two methods for the construction of the decomposition. One is the moduli space approach following the work of Kuznetsov on the sextic del Pezzo fibrations and the components are given by the derived categories of fine relative moduli spaces. The other approach is that one can realize the fibration as a linear section of a Grassmannian bundle and apply homological projective duality.

scholarly journals GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON ℂℙ2 OF DEGREE 2

2010 ◽  
Vol 53 (1) ◽  
pp. 153-168 ◽  
Author(s):  
CLAUDIA R. ALCÁNTARA
Keyword(s):  
Moduli Space ◽  
Invariant Theory ◽  
Geometric Invariant Theory ◽  
Del Pezzo Surfaces ◽  
Holomorphic Foliations ◽  
Geometric Invariant ◽  
Linear Action ◽  
Unstable Foliation ◽  
Rational Fibration ◽  
Del Pezzo

AbstractLet 2 be the space of the holomorphic foliations on ℂℙ2 of degree 2. In this paper we study the linear action PGL(3, ℂ) × 2 → 2 given by gX = DgX ^(g−1) in the sense of the Geometric Invariant Theory. We obtain a characterisation of unstable and stable foliations according to properties of singular points and existence of invariant lines. We also prove that if X is an unstable foliation of degree 2, then X is transversal with respect to a rational fibration. Finally we prove that the geometric quotient of non-degenerate foliations without invariant lines is the moduli space of polarised del Pezzo surfaces of degree 2.

Weakly exceptional singularities of log del Pezzo surfaces

2019 ◽  
Vol 30 (01) ◽  
pp. 1950010
Author(s):  
In-Kyun Kim ◽  
Joonyeong Won
Keyword(s):  
Complete Intersection ◽  
Projective Spaces ◽  
Pezzo Surface ◽  
Del Pezzo Surfaces ◽  
Del Pezzo Surface ◽  
Log Canonical ◽  
Del Pezzo ◽  
Log Del Pezzo Surfaces

We complete the computation of global log canonical thresholds, or equivalently alpha invariants, of quasi-smooth well-formed complete intersection log del Pezzo surfaces of amplitude 1 in weighted projective spaces. As an application, we prove that they are weakly exceptional. And we investigate the super-rigid affine Fano 3-folds containing a log del Pezzo surface as boundary.

Log Canonical Thresholds of Complete Intersection Log Del Pezzo Surfaces

2015 ◽  
Vol 58 (2) ◽  
pp. 445-483 ◽  
Author(s):  
In-Kyun Kim ◽  
Jihun Park
Keyword(s):  
Complete Intersection ◽  
Einstein Metrics ◽  
Projective Spaces ◽  
Del Pezzo Surfaces ◽  
Log Canonical ◽  
Del Pezzo ◽  
Kähler Einstein Metrics ◽  
Log Del Pezzo Surfaces

AbstractWe compute the global log canonical thresholds of quasi-smooth well-formed complete intersection log del Pezzo surfaces of amplitude 1 in weighted projective spaces. As a corollary we show the existence of orbifold Kähler—Einstein metrics on many of them.

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