Asymptotic Hodge theory of vector bundles

Nonlinear Hodge equations in vector bundles

A gauge-invariant form of the nonlinear Hodge equations is studied. 1991 MSC: 58E15 (Classical field theory)

Higgs Bundles and Non-abelian Hodge Theory

Asymptotic Hodge theory and quantum products

Assuming suitable convergence properties for the Gromov-Witten potential of a Calabi-Yau manifold X, one may construct a polarized variation of Hodge structure over the complexified Kähler cone of X. In this paper we show that, in the case of fourfolds, there is a correspondence between “quantum potentials” and polarized variations of Hodge structures that degenerate to a maximally unipotent bo...

Hodge Style Chern Classes for Vector Bundles on Schemes

In this note, we develop the formalism of Hodge style chern classes of vector bundles over arbitrary quasi-projective schemes defined over K, a field of characteristic zero. The theory of Chern classes is well known by now and without any restriction on the characteristic, can be defined in many theories with rational coefficients, like for example the Chow ring. Atiyah [1] developed the theory...

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 ...