scholarly journals Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces

2014 ◽  
Vol 176 (1) ◽  
pp. 241-269 ◽  
Author(s):  
Martijn Kool
Keyword(s):  
Moduli Spaces ◽  
Euler Characteristics ◽  
Toric Surfaces ◽  
Torsion Free

scholarly journals Instantons, Topological Strings, and Enumerative Geometry

2010 ◽  
Vol 2010 ◽  
pp. 1-70 ◽  
Author(s):  
Richard J. Szabo
Keyword(s):  
Moduli Spaces ◽  
Gauge Theories ◽  
Topological String ◽  
Two Dimensions ◽  
Enumerative Geometry ◽  
Topological String Theory ◽  
Euler Characteristics ◽  
Wall Crossing ◽  
Supersymmetric Gauge ◽  
Torsion Free

We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories in six, four, and two dimensions which naturally arise in the context of topological string theory on certain noncompact threefolds. We describe how the instanton counting in these gauge theories is related to the computation of the entropy of supersymmetric black holes and how these results are related to wall-crossing properties of enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants. Some features of moduli spaces of torsion-free sheaves and the computation of their Euler characteristics are also elucidated.

Elementary amenable groups and 4-manifolds with Euler characteristic 0

1991 ◽  
Vol 50 (1) ◽  
pp. 160-170 ◽  
Author(s):  
Jonathan A. Hillman
Keyword(s):  
Normal Subgroup ◽  
Fundamental Group ◽  
Euler Characteristic ◽  
Fundamental Groups ◽  
Normal Subgroups ◽  
Euler Characteristics ◽  
Amenable Groups ◽  
Amenable Subgroup ◽  
Finite Subgroups ◽  
Torsion Free

AbstractWe extend earlier work relating asphericity and Euler characteristics for finite complexes whose fundamental groups have nontrivial torsion free abelian normal subgroups. In particular a finitely presentable group which has a nontrivial elementary amenable subgroup whose finite subgroups have bounded order and with no nontrivial finite normal subgroup must have deficiency at most 1, and if it has a presentation of deficiency 1 then the corresponding 2-complex is aspherical. Similarly if the fundamental group of a closed 4-manifold with Euler characteristic 0 is virtually torsion free and elementary amenable then it either has 2 ends or is virtually an extension of Z by a subgroup of Q, or the manifold is asphencal and the group is virtually poly- Z of Hirsch length 4.

Exotic Holonomies ${\rm E}^{(a)}_7$

1997 ◽  
Vol 08 (05) ◽  
pp. 583-594 ◽  
Author(s):  
Quo-Shin Chi ◽  
Sergey Merkulov ◽  
Lorenz Schwachhöfer
Keyword(s):  
Symmetry Group ◽  
Lie Groups ◽  
Lie Group ◽  
Moduli Spaces ◽  
Local Symmetry ◽  
Positive Dimension ◽  
Affine Connections ◽  
Finite Dimensional ◽  
Torsion Free

It is proved that the Lie groups [Formula: see text] and [Formula: see text] represented in ℝ56 and the Lie group [Formula: see text] represented in ℝ112 occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of positive dimension.

scholarly journals Perverse bundles and Calogero–Moser spaces

2008 ◽  
Vol 144 (6) ◽  
pp. 1403-1428 ◽  
Author(s):  
David Ben-Zvi ◽  
Thomas Nevins
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Hilbert Schemes ◽  
Simple Description ◽  
Quiver Varieties ◽  
Complex Curves ◽  
Noncommutative Version ◽  
Cotangent Bundles ◽  
Rank One ◽  
Torsion Free

AbstractWe present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in the rank-one case). The proof is based on the description of the derived category of 𝒟-modules on X by a noncommutative version of the Beilinson transform on P1.

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.

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