Weil-Petersson metric in the moduli space of compact polarized K�hler-Einstein manifolds of zero first Chern class

1986 ◽  
Vol 54 (4) ◽  
pp. 405-438 ◽  
Author(s):  
Antonella Nannicini
Keyword(s):  
Moduli Space ◽  
Chern Class ◽  
Einstein Manifolds ◽  
First Chern Class

Symplectic Geometry of the Moduli Space of Flat Connections on a Riemann Surface: Inductive Decompositions and Vanishing Theorems

2000 ◽  
Vol 52 (3) ◽  
pp. 582-612 ◽  
Author(s):  
Lisa C. Jeffrey ◽  
Jonathan Weitsman
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Chern Class ◽  
Boundary Component ◽  
Symplectic Geometry ◽  
Line Bundles ◽  
Vanishing Theorems ◽  
Stable Bundles ◽  
Flat Connections ◽  
First Chern Class

AbstractThis paper treats the moduli space g,1(Λ) of representations of the fundamental group of a Riemann surface of genus g with one boundary component which send the loop around the boundary to an element conjugate to exp Λ, where Λ is in the fundamental alcove of a Lie algebra. We construct natural line bundles over g,1(Λ) and exhibit natural homology cycles representing the Poincaré dual of the first Chern class. We use these cycles to prove differential equations satisfied by the symplectic volumes of these spaces. Finally we give a bound on the degree of a nonvanishing element of a particular subring of the cohomology of the moduli space of stable bundles of coprime rank k and degree d.

scholarly journals GAUGE-EQUIVARIANT HILBERT BIMODULES AND CROSSED PRODUCTS BY ENDOMORPHISMS

2009 ◽  
Vol 20 (11) ◽  
pp. 1363-1396 ◽  
Author(s):  
EZIO VASSELLI
Keyword(s):  
Vector Bundle ◽  
Moduli Space ◽  
Chern Class ◽  
Vector Bundles ◽  
Crossed Products ◽  
Tensor Categories ◽  
Dual Object ◽  
Nontrivial Center ◽  
First Chern Class ◽  
The Given

C*-endomorphisms arising from superselection structures with nontrivial center define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz–Pimsner algebra of a vector bundle having the above-mentioned rank, first Chern class and can be used to construct a duality for abstract (nonsymmetric) tensor categories versus group bundles acting on (nonsymmetric) Hilbert bimodules. Existence and unicity of the dual object (i.e. the 'gauge' group bundle) are not ensured: we give a description of this phenomenon in terms of a certain moduli space associated with the given endomorphism. The above-mentioned Hilbert bimodules are noncommutative analogs of gauge-equivariant vector bundles in the sense of Nistor–Troitsky.

scholarly journals The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class

2021 ◽  
Vol 9 ◽  
Author(s):  
Patrick Graf ◽  
Martin Schwald
Keyword(s):  
Chern Class ◽  
Cohomology Group ◽  
Canonical Bundle ◽  
Deformation Space ◽  
Projective Varieties ◽  
Quotient Singularities ◽  
Finite Quotient ◽  
First Chern Class ◽  
Small Deformations

Abstract Let X be a normal compact Kähler space with klt singularities and torsion canonical bundle. We show that X admits arbitrarily small deformations that are projective varieties if its locally trivial deformation space is smooth. We then prove that this unobstructedness assumption holds in at least three cases: if X has toroidal singularities, if X has finite quotient singularities and if the cohomology group ${\mathrm {H}^{2} \!\left ( X, {\mathscr {T}_{X}} \right )}$ vanishes.

scholarly journals First Chern class and birational germs of Kato surfaces

2018 ◽  
Vol 12 (1-2) ◽  
pp. 239-249
Author(s):  
Massimiliano Pontecorvo
Keyword(s):  
Chern Class ◽  
First Chern Class ◽  
Kato Surfaces

The First Chern Class of the Verlinde Bundles

2015 ◽  
pp. 87-111 ◽  
Author(s):  
Alina Marian ◽  
Dragos Oprea ◽  
Rahul Pandharipande
Keyword(s):  
Chern Class ◽  
First Chern Class

Topological invariance of the Hall conductance and quantization

2015 ◽  
Vol 29 (24) ◽  
pp. 1550135
Author(s):  
Paul Bracken
Keyword(s):  
Chern Class ◽  
Fiber Bundle ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Hall Conductance ◽  
Integer Multiple ◽  
Principal Fiber Bundle ◽  
Topological Invariance ◽  
First Chern Class

It is shown that the Kubo equation for the Hall conductance can be expressed as an integral which implies quantization of the Hall conductance. The integral can be interpreted as the first Chern class of a [Formula: see text] principal fiber bundle on a two-dimensional torus. This accounts for the conductance given as an integer multiple of [Formula: see text]. The formalism can be extended to deduce the fractional conductivity as well.

scholarly journals Kähler–Ricci solitons on toric manifolds with positive first Chern class

2004 ◽  
Vol 188 (1) ◽  
pp. 87-103 ◽  
Author(s):  
Xu-Jia Wang ◽  
Xiaohua Zhu
Keyword(s):  
Chern Class ◽  
Ricci Solitons ◽  
Toric Manifolds ◽  
First Chern Class

scholarly journals Families of K-3 Surfaces

1972 ◽  
Vol 48 ◽  
pp. 1-17 ◽  
Author(s):  
Alan L. Mayer
Keyword(s):  
Complex Manifold ◽  
Chern Class ◽  
Compact Complex Manifold ◽  
Canonical Sheaf ◽  
First Chern Class

Let V be a 2-dimensional compact complex manifold. V is called a K-3 surface if : a) the irregularity q = dim H1(V, θ) of V vanishes and b) the first Chern class c1 of V vanishes. The canonical sheaf (of holo-morphic 2-forms) K of such a surface is trivial, since q = 0 implies that the Chern class map cx : Pic (V) → H2(V, Z) is injective : thus V has a nowhere zero holomorphic 2-form.

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