Instanton Moduli as a Novel Map from Tori to K3-Surfaces

P J BRAAM, A MACIOCIA, A TODOROV

Research output: Contribution to journalArticlepeer-review

Abstract

A map is constructed from the moduli of hyper-Kahler tori to hyper-Kahler K3 surfaces which does not coincide with the Kummer map. The map takes a torus to the moduli space of SO(3) connections on a bundle with nontrivial first Stiefel-Whitney class and first Pontrjagin class equal to -4. This map is shown to intersect the Kummer moduli and also certain subvarieties of singular K3 surfaces. Our map is shown to satisfy the local Torelli theorem, and the K3-surfaces in its image are shown to carry a natural metric which is Calabi-Yau.

Original languageEnglish
Pages (from-to)419-451
Number of pages33
JournalInventiones mathematicae
Volume108
Issue number2
Publication statusPublished - May 1992

Keywords

  • YANG-MILLS CONNECTIONS
  • SELF-DUAL CONNECTIONS
  • K3 SURFACES
  • 4-MANIFOLDS
  • MANIFOLDS
  • BUNDLES
  • SPACE
  • CONSTRUCTION
  • CURVATURE
  • GEOMETRY

Cite this