Numerical Hermitian Yang-Mills connections and Kähler cone substructure

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kähler cone substructure on manifolds with h1;1  > 1. Since the computation depends only on a one-dimensional ray in the Kähler moduli space, it can probe slope-stability regardless of the size of h1;1. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kähler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, a rapid computational check is proposed for probing the slope-stable stability properties of a given vector bundle.