Stability of complex vector bundles

Stability of Vector Bundles From F-theory

We use a recently proposed formulation of stable holomorphic vector bundles V on elliptically fibered Calabi–Yau n-fold Zn in terms of toric geometry to describe stability conditions on V . Using the toric map f : Wn+1 → (V, Zn) that identifies dual pairs of F-theory/heterotic duality we show how stability can be related to the existence of holomorphic sections of a certain line bundle that is ...

Weak Equivalence Classes of Complex Vector Bundles

For any complex vector bundle Ek of rank k over a manifold Mm with Chern classes ci ∈ H2i(Mm, Z) and any non-negative integers l1, · · · , lk we show the existence of a positive number p(m, k) and the existence of a complex vector bundle Êk over Mm whose Chern classes are p(m, k) · li · ci ∈ H2i(Mm, Z). We also discuss a version of this statement for holomorphic vector bundles over projective a...

Differential Geometry of Complex Vector Bundles

Complex Vector Bundles and Jacobi Forms

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi–Yau manifold. In physics such a function appears as the partition function of N = 2 superconformal field theories. In these notes we define the modified ...

Stability of Tautological Vector Bundles on Hilbert Squares of Surfaces

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes. Let S be a smooth, projective surface, let Hilb(S) be the Hilbert scheme parametrizing subschemes of S of length 2. It is known by a classical theorem of Fogarty [Fo] that Hilb(S) is a smooth, projective variety of dimension 4. Let Z ⊂ S × H...