Anti-self-dual bihermitian structures on Inoue surfaces

2009/03/09 by A. Fujiki, Fujiki, A., M. Pontecorvo +1
Mathematics · #32G05 (Secondary) #53C55 (Primary) 53C28 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG #msc:32G05 #msc:53C28 #msc:53C55

paper · pdf · doi:10.48550/arxiv.0903.1320

69 pages,

arxiv created 2009/03/09 · arxiv updated 2009/12/01

Abstract

We show that any hyperbolic Inoue surface (or Inoue-Hirzebruch surface of even type) admits anti-self-dual bihermitian structures. The same result also holds for any of its small deformations as far as its anti-canonical system is non-empty. Similar results are obtained for parabolic Inoue surfaces. Our method also yields anti-self-dual hermitian metrics on any half Inoue surface. We use the twistor method of Donaldson-Friedman for the proof.

Related

• Para-hyperhermitian surfaces
• Bihermitian metrics on Del Pezzo surfaces
• Bihermitian metrics on Hopf surfaces
• Anti-self-dual blowups II
• Uniqueness of birational structures on Inoue surfaces