Seminarium KMMF "Teoria Dwoistości"

We study moduli spaces of stable (in the sense of geometric invariant theory) vector bundles on Riemann surfaces. We report on the current state of the Brill—Noether problem that classifies bundles with global sections (i.e. non-trivial vector fields). We show various examples (including Higgs bundles), calculations of numerical invariants and specific bundle constructions