scholarly journals Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces

2009 ◽  
Vol 178 (1) ◽  
pp. 173-227 ◽  
Author(s):  
Paul Hacking ◽  
Sean Keel ◽  
Jenia Tevelev
Keyword(s):  
Moduli Spaces ◽  
Del Pezzo Surfaces ◽  
Stable Pair ◽  
Log Canonical ◽  
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.

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.

scholarly journals Log-canonical thresholds on del Pezzo surfaces of degrees ≥ 2

2010 ◽  
Vol 200 ◽  
pp. 1-26
Author(s):  
Jihun Park ◽  
Joonyeong Won
Keyword(s):  
Del Pezzo Surfaces ◽  
Log Canonical ◽  
Del Pezzo

AbstractWe compute the global log-canonical thresholds (lct) of del Pezzo surfaces of degrees ≥ 2 with du Val singularities.

Sign in / Sign up

Export Citation Format

Share Document