Viktoria Heu

Hitchin Hamiltonians in Genus 2

We give an explicit expression of the Hitchin Hamiltonian system for rank two vector bundles with trivial determinant bundle over a curve of genus two.

Isomonodromic Deformations and Very Stable Vector Bundles of Rank Two

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this universal deformation. In a previous work we proved that the vector bundle corresponding to a general parameter of this family is stable. Here we prove that the vector bundle corresponding to a general parameter is in fact very stable, meaning it does not admit any nonzero nilpotent Higgs field.

Non-flat extension of flat vector bundles

We construct a pair (E,F), where E is a holomorphic vector bundle over a compact Riemann surface and F ⊂ E a holomorphic subbundle, such that both F and E/F admit holomorphic connections, but E does not.