scholarly journals Analytic Moduli Spaces of Simple (Co)Framed Sheaves

2002 ◽  
pp. 99-109
Author(s):  
Hubert Flenner ◽  
Martin Lübke
Keyword(s):  
Moduli Spaces ◽  
Framed Sheaves

Corrigendum and addendum to “Moduli spaces of framed sheaves and quiver varieties”

2017 ◽  
Vol 121 ◽  
pp. 176-179
Author(s):  
Claudio Bartocci ◽  
Valeriano Lanza ◽  
Claudio L.S. Rava
Keyword(s):  
Moduli Spaces ◽  
Quiver Varieties ◽  
Framed Sheaves

scholarly journals Birational geometry of moduli spaces of perverse coherent sheaves on blow-ups

2021 ◽  
Author(s):  
Naoki Koseki
Keyword(s):  
Moduli Spaces ◽  
Blow Up ◽  
Derived Categories ◽  
Model Program ◽  
Minimal Model Program ◽  
Blow Down ◽  
Coherent Sheaves ◽  
Framed Sheaves ◽  
Wall Crossing Formula ◽  
Torsion Free

AbstractIn order to study the wall-crossing formula of Donaldson type invariants on the blown-up plane, Nakajima–Yoshioka constructed a sequence of blow-up/blow-down diagrams connecting the moduli space of torsion free framed sheaves on projective plane, and that on its blow-up. In this paper, we prove that Nakajima–Yoshioka’s diagram realizes the minimal model program. Furthermore, we obtain a fully-faithful embedding between the derived categories of these moduli spaces.

scholarly journals MODULI SPACES OF FRAMED SHEAVES ON CERTAIN RULED SURFACES OVER ELLIPTIC CURVES

2002 ◽  
Vol 13 (10) ◽  
pp. 1117-1151 ◽  
Author(s):  
THOMAS A. NEVINS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Fixed Point Set ◽  
Explicit Formulas ◽  
Rational Homology ◽  
Moduli Stack ◽  
Framed Sheaves ◽  
Fixed Reference ◽  
Point Set ◽  
Projective Completion

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve C; we study the moduli problem of parametrizing certain pairs consisting of a sheaf ℰ on S and a map of ℰ to a fixed reference sheaf on S. We prove that the full moduli stack for this problem is representable by a scheme in some cases. Moreover, the moduli stack admits an action by the group C*, and we determine its fixed-point set, which leads to explicit formulas for the rational homology of the moduli space.

scholarly journals Monads for framed sheaves on Hirzebruch surfaces

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Claudio Bartocci ◽  
Claudio L. S. Rava ◽  
Ugo Bruzzo
Keyword(s):  
Moduli Spaces ◽  
Algebraic Varieties ◽  
Hirzebruch Surfaces ◽  
Framed Sheaves ◽  
Torsion Free

AbstractWe define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.

scholarly journals Moduli spaces of framed sheaves and quiver varieties

2017 ◽  
Vol 118 ◽  
pp. 20-39 ◽  
Author(s):  
Claudio Bartocci ◽  
Valeriano Lanza ◽  
Claudio L.S. Rava
Keyword(s):  
Moduli Spaces ◽  
Quiver Varieties ◽  
Framed Sheaves

scholarly journals Framed sheaves on projective space and Quot schemes

2021 ◽  
Author(s):  
Alberto Cazzaniga ◽  
Andrea T. Ricolfi
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Chern Character ◽  
Free Sheaf ◽  
Quot Scheme ◽  
Quot Schemes ◽  
Framed Sheaves ◽  
Torsion Free

AbstractWe prove that, given integers $$m\ge 3$$ m ≥ 3 , $$r\ge 1$$ r ≥ 1 and $$n\ge 0$$ n ≥ 0 , the moduli space of torsion free sheaves on $${\mathbb {P}}^m$$ P m with Chern character $$(r,0,\ldots ,0,-n)$$ ( r , 0 , … , 0 , - n ) that are trivial along a hyperplane $$D \subset {\mathbb {P}}^m$$ D ⊂ P m is isomorphic to the Quot scheme $$\mathrm{Quot}_{{\mathbb {A}}^m}({\mathscr {O}}^{\oplus r},n)$$ Quot A m ( O ⊕ r , n ) of 0-dimensional length n quotients of the free sheaf $${\mathscr {O}}^{\oplus r}$$ O ⊕ r on $${\mathbb {A}}^m$$ A m . The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

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