Geometry of rational double points

• Applicant: Professor Dr. Christian Liedtke
• Subject Area: Mathematics
• Term: from 2019 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 424829246

• Final Report Year: 2023

Final Report Abstract

In this project, a classification of weak del Pezzo surfaces with global vector fields over algebraically closed fields of arbitrary characteristic was achieved, as well as a similar classification for RDP del Pezzo surfaces in odd characteristics. Moreover, the connected components of the automorphism schemes and the spaces of global vector fields of these surfaces were determined. These results are important for the classification of algebraic surfaces, but also in view of Mori fibre spaces of relative dimension 2 in the minimal model programme. They are also connected to the deformation theory of the RDPs that occur on RDP del Pezzo surfaces in positive characteristic, a classification that was also achieved in the course of this project.

Publications

• Which rational double points occur on del Pezzo surfaces?. Épijournal de Géométrie Algébrique, Volume 5.
  Stadlmayr, Claudia
  
• Geometry of rational double points and del Pezzo surfaces, Ph.D. thesis, Technische Universität München (2022/23).
  C. Stadlmayr
  
• RDP del Pezzo surfaces with global vector fields in odd characteristic. Algebraic Geometry, 346-385.
  Martin, Gebhard & Stadlmayr, Claudia
  
• Weak del Pezzo surfaces with global vector fields. Geometry & Topology, 28(8), 3565-3641.
  Martin, Gebhard & Stadlmayr, Claudia