Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure

Understand

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 Kahler cone substructure on manifolds with h^{1,1}>1.
• Since the computation depends only on a one-dimensional ray in the Kahler moduli space, it can probe slope-stability regardless of the size of h^{1,1}.
• Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kahler moduli space.