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

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.

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 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.

Topological Invariants and Differential Geometry

2017 ◽  
Author(s):  
Paula Tretkoff
Keyword(s):  
Differential Geometry ◽  
Topological Space ◽  
Chern Class ◽  
Euler Number ◽  
Line Bundles ◽  
Topological Invariants ◽  
Fundamental Groups ◽  
Hermitian Metrics ◽  
Finite Set ◽  
First Chern Class

This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering spaces and some basics of the theory of complex manifolds and Hermitian metrics, including the concept of real manifold. Finally, it provides some general facts about divisors, line bundles, and the first Chern class on a complex manifold X.

scholarly journals Contact homology of good toric contact manifolds

2011 ◽  
Vol 148 (1) ◽  
pp. 304-334 ◽  
Author(s):  
Miguel Abreu ◽  
Leonardo Macarini
Keyword(s):  
Homotopy Class ◽  
Chern Class ◽  
Einstein Metrics ◽  
Contact Manifold ◽  
Infinite Family ◽  
Contact Structures ◽  
Contact Homology ◽  
Contact Manifolds ◽  
First Chern Class ◽  
Toric Contact Manifolds

AbstractIn this paper we show that any good toric contact manifold has a well-defined cylindrical contact homology, and describe how it can be combinatorially computed from the associated moment cone. As an application, we compute the cylindrical contact homology of a particularly nice family of examples that appear in the work of Gauntlett et al. on Sasaki–Einstein metrics. We show in particular that these give rise to a new infinite family of non-equivalent contact structures on S2×S3 in the unique homotopy class of almost contact structures with vanishing first Chern class.

scholarly journals MIRROR SYMMETRY AND STRING VACUA FROM A SPECIAL CLASS OF FANO VARIETIES

1996 ◽  
Vol 11 (17) ◽  
pp. 3049-3096 ◽  
Author(s):  
ROLF SCHIMMRIGK
Keyword(s):  
Chern Class ◽  
Mirror Symmetry ◽  
Central Charge ◽  
Mean Field ◽  
Fano Varieties ◽  
Complex Dimension ◽  
Crucial Information ◽  
First Chern Class ◽  
The One ◽  
Calabi Yau Manifolds

Because of the existence of rigid Calabi-Yau manifolds, mirror symmetry cannot be understood as an operation on the space of manifolds with vanishing first Chern class. In this article I continue to investigate a particular type of Kähler manifolds with positive first Chern class which generalize Calabi-Yau manifolds in a natural way and which provide a framework for mirrors of rigid string vacua. This class comprises Fano manifolds of a special type which encode crucial information about ground states of the superstring. It is shown in particular that the massless spectra of (2, 2)-supersymmetric vacua of central charge ĉ=D crit can be derived from special Fano varieties of complex dimension D crit +2(Q−1), Q>1, and that in certain circumstances it is even possible to embed Calabi-Yau manifolds into such higher dimensional spaces. The constructions described here lead to new insight into the relation between exactly solvable models and their mean field theories on the one hand and their corresponding Calabi-Yau manifolds on the other. Furthermore it is shown that Witten’s formulation of the Landau-Ginzburg/Calabi-Yau relation can be applied to the present framework as well.

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