O’Grady’s birational maps and strange duality via wall-hitting

2019 ◽  
Vol 30 (09) ◽  
pp. 1950044
Author(s):  
Huachen Chen
Keyword(s):  
Moduli Spaces ◽  
Hodge Structure ◽  
Duke Math ◽  
K3 Surface ◽  
Birational Maps ◽  
Moduli Spaces Of Sheaves ◽  
Wall Crossing ◽  
Moduli Of Sheaves ◽  
Ideal Sheaves ◽  
Strange Duality

We prove that O’Grady’s birational maps [K. G O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebr. Geom. 6(4) (1997) 599–644] between moduli of sheaves on an elliptic K3 surface can be interpreted as intermediate wall-crossing (wall-hitting) transformations at so-called totally semistable walls, studied by Bayer and Macrì [A. Bayer and E. Macrì, MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations, Inventiones Mathematicae 198(3) (2014) 505–590]. As a key ingredient, we describe the first totally semistable wall for ideal sheaves of [Formula: see text] points on the elliptic [Formula: see text]. As an application, we give new examples of strange duality isomorphisms, based on a result of Marian and Oprea [A. Marian and D. Oprea, Generic strange duality for K3 surfaces, with an appendix by Kota Yoshioka, Duke Math. J. 162(8) (2013) 1463–1501].

SEMISTABLE SHEAVES WITH SYMMETRIC ON A QUADRIC SURFACE

2016 ◽  
Vol 227 ◽  
pp. 86-159 ◽  
Author(s):  
TAKESHI ABE
Keyword(s):  
Projective Plane ◽  
Moduli Spaces ◽  
Rational Maps ◽  
Quadric Surface ◽  
Plane Case ◽  
Moduli Spaces Of Sheaves ◽  
Strange Duality

For moduli spaces of sheaves with symmetric $c_{1}$ on a quadric surface, we pursue analogy to some results known for moduli spaces of sheaves on a projective plane. We define an invariant height, introduced by Drezet in the projective plane case, for moduli spaces of sheaves with symmetric $c_{1}$ on a quadric surface and describe the structure of moduli spaces of height zero. Then we study rational maps of moduli spaces of positive height to moduli spaces of representation of quivers, effective cones of moduli spaces, and strange duality for height-zero moduli spaces.

scholarly journals Change of Polarization for Moduli of Sheaves on Surfaces as Bridgeland Wall-crossing

2018 ◽  
Vol 2020 (7) ◽  
pp. 2007-2033
Author(s):  
Aaron Bertram ◽  
Cristian Martinez
Keyword(s):  
Moduli Spaces ◽  
Stability Conditions ◽  
One Dimensional ◽  
Wall Crossing ◽  
Moduli Of Sheaves ◽  
Twisted Sheaves

Abstract We prove that the “Thaddeus flips” of L-twisted sheaves constructed by Matsuki and Wentworth explaining the change of polarization for Gieseker semistable sheaves on a surface can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of polarization for moduli spaces of one-dimensional Gieseker semistable sheaves on a surface by varying a family of stability conditions.

scholarly journals Intersection cohomology of moduli spaces of sheaves on surfaces

2018 ◽  
Vol 24 (5) ◽  
pp. 3889-3926 ◽  
Author(s):  
Jan Manschot ◽  
Sergey Mozgovoy
Keyword(s):  
Moduli Spaces ◽  
Intersection Cohomology ◽  
Moduli Spaces Of Sheaves

scholarly journals The ample cone of moduli spaces of sheaves on the plane

2016 ◽  
Vol 3 (1) ◽  
pp. 106-136 ◽  
Author(s):  
Izzet Coskun ◽  
Jack Huizenga
Keyword(s):  
Moduli Spaces ◽  
Moduli Spaces Of Sheaves ◽  
Ample Cone

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].

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