scholarly journals Projectivity of Bridgeland Moduli Spaces on Del Pezzo Surfaces of Picard Rank 2

2016 ◽  
pp. rnw132
Author(s):  
Daniele Arcara ◽  
Eric Miles
Keyword(s):  
Moduli Spaces ◽  
Del Pezzo Surfaces ◽  
Rank 2 ◽  
Del Pezzo

scholarly journals Local BPS Invariants: Enumerative Aspects and Wall-Crossing

2018 ◽  
Vol 2020 (17) ◽  
pp. 5450-5475 ◽  
Author(s):  
Jinwon Choi ◽  
Michel van Garrel ◽  
Sheldon Katz ◽  
Nobuyoshi Takahashi
Keyword(s):  
Projective Space ◽  
Euler Characteristic ◽  
Moduli Spaces ◽  
Del Pezzo Surfaces ◽  
Arithmetic Genus ◽  
One Dimensional ◽  
Wall Crossing ◽  
Bps Invariants ◽  
Del Pezzo ◽  
Dimensional Projective Space

Abstract We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincaré polynomials of the moduli spaces for the curve classes $\beta $ having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of $((-K_S).\beta -1)$-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].

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 THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

2020 ◽  
pp. 1-23
Author(s):  
MICHELE BOLOGNESI ◽  
NÉSTOR FERNÁNDEZ VARGAS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Hyperelliptic Curve ◽  
Geometric Description ◽  
Birational Model ◽  
Rank 2 ◽  
Semistable Vector Bundles ◽  
Ramification Locus

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

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 Tropicalization of del Pezzo surfaces

2016 ◽  
Vol 300 ◽  
pp. 156-189 ◽  
Author(s):  
Qingchun Ren ◽  
Kristin Shaw ◽  
Bernd Sturmfels
Keyword(s):  
Del Pezzo Surfaces ◽  
Del Pezzo
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