Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 1)

Andrei Teleman (1) , Robert Binder (2) , Fanny Bastien (2)

1 I2M - Institut de Mathématiques de Marseille
2 IF - Institut Fourier

This series of lectures is dedicated to recent results concerning the existence of holomorphic curves on the surfaces of class VII. The first lecture will be an introduction to the Donaldson theory. We will present the fundamental notions and some important results in the theory, explaining ideas of the proofs. In the second lecture we will present the theory of holomorphic fiber bundles on complex surfaces, the stability notion, moduli spaces and the Kobayashi-Hitschin correspondence that links moduli spaces of stable fiber bundles (defined in the fram of complex geometry) to moduli spaces of instantons (defined in the frame of the Donaldson theory). In the last two lectures we will prove the existence of holomorphic curves on minimal surfaces of class VII with b2=1 or 2 and we will present the general strategy and the last results obtained in the general case.

Mots clés: summer school 2012; foliations; pseudoholomorphic curves; instantons; holomorphic curves; surfaces of class VII

Mots clés: eem2012; école d’été 2012; grenoble; feuilletages; courbes pseudoholomorphes; applications

Domaines: Mathématiques [math]

Andrei Teleman, Robert Binder, Fanny Bastien. Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 1) : Summer School 2012 - Foliations, Pseudoholomorphic curves, Applications . 2012. ⟨medihal-01320569⟩