Geometri- och topologiseminarium: Classification of full exceptional collections of line bundles on three blow-ups of P^3 and on some projective bundles

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Wanmin Liu (IBS Center for Geometry and Physics)
  • Kontaktperson: Maksim Maydanskiy
  • Seminarium

Abstract: A fullness conjecture of Kuznetsov says that if a smooth projective variety X admits a full exceptional collection of line bundles of length l, then any exceptional collection of line bundles of length l is full. In this talk, we show that this conjecture holds for X as the blow-up of P^3 at a point, a line, or a twisted cubic curve, i.e. any exceptional collection of line bundles of length 6 on X is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such X. The preprint is available at IBS-CGP preprint [CGP17025].

I will also introduce some recent progress on some projective bundles, including blow-up of P^n at a point. This is a joint work with Song Yang and Xun Yu at Tianjin University.