Complex geometric applications of Gauge Theory

Andrei Teleman (1) , Matei Toma (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 IMAR - "Simion Stoilow" Institute of Mathematics

We show that Donaldson theory can be used to solve a classical problem in complex geometry: which topological vector bundles on a given complex surface admit a holomorphic structure? The problem is interesting for non-algebraic surfaces. We answer completely this question for bundles of rank 2 over a K3 surface.

Domaines: Variables complexes [math.CV]; Géométrie différentielle [math.DG]; Topologie géométrique [math.GT]

Andrei Teleman, Matei Toma. Complex geometric applications of Gauge Theory. Komplexe Analysis, Aug 2004, Oberwolfach, Germany. pp.2204-2207, ⟨10.4171/OWR/2004/42⟩. ⟨hal-00881720⟩