$1$-point Gromov-Witten invariants of the moduli spaces of sheaves over the projective plane

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.

Download Full-text

Obstruction theory for moduli spaces of framed flags of sheaves on the projective plane

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2021.104255 ◽

2021 ◽

pp. 104255

Author(s):

Rodrigo A. von Flach ◽

Marcos Jardim ◽

Valeriano Lanza

Keyword(s):

Projective Plane ◽

Moduli Spaces ◽

Obstruction Theory

Download Full-text

Poisson structures on moduli spaces of sheaves over Poisson surfaces

Inventiones mathematicae ◽

10.1007/bf01884307 ◽

1995 ◽

Vol 121 (1) ◽

pp. 421-436 ◽

Cited By ~ 22

Author(s):

Francesco Bottacin

Keyword(s):

Moduli Spaces ◽

Poisson Structures ◽

Moduli Spaces Of Sheaves

Download Full-text

Intersection cohomology of moduli spaces of sheaves on surfaces

Selecta Mathematica ◽

10.1007/s00029-018-0431-1 ◽

2018 ◽

Vol 24 (5) ◽

pp. 3889-3926 ◽

Cited By ~ 3

Author(s):

Jan Manschot ◽

Sergey Mozgovoy

Keyword(s):

Moduli Spaces ◽

Intersection Cohomology ◽

Moduli Spaces Of Sheaves

Download Full-text

On the Singular Sheaves in the Fine Simpson Moduli Spaces of 1-dimensional Sheaves

Canadian Mathematical Bulletin ◽

10.4153/cmb-2016-059-7 ◽

2017 ◽

Vol 60 (3) ◽

pp. 522-535 ◽

Cited By ~ 1

Author(s):

Oleksandr Iena ◽

Alain Leytem

Keyword(s):

Projective Plane ◽

Moduli Space ◽

Moduli Spaces ◽

Blow Up ◽

Line Bundles ◽

Hilbert Polynomial ◽

Stable Sheaves ◽

Closed Subvariety

AbstractIn the Simpson moduli space M of semi-stable sheaves with Hilbert polynomial dm − 1 on a projective plane we study the closed subvariety M' of sheaves that are not locally free on their support. We show that for d ≥4 , it is a singular subvariety of codimension 2 in M. The blow up of M along M' is interpreted as a (partial) modification of M \ M' by line bundles (on support).

Download Full-text