Geometry of moduli space of sheaves on del Pezzo surfaces via Maruyama transform

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

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Derived categories of quintic del Pezzo fibrations

Selecta Mathematica ◽

10.1007/s00029-020-00615-0 ◽

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.

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GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON ℂℙ2 OF DEGREE 2

Glasgow Mathematical Journal ◽

10.1017/s0017089510000674 ◽

2010 ◽

Vol 53 (1) ◽

pp. 153-168 ◽

Cited By ~ 2

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.

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