Exceptional sequences on toric varieties of Picard rank 3

• Applicant: Professor Dr. Frederik Witt
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 511402593

The bounded derived category of coherent sheaves is one of the most important invariants of a smooth projective variety. In this context, finding and classifying so-called full exceptional sequences of line bundles has been an active area of research ever since Beilinson used such sequences to describe the derived category of projective space. In his 2014 ICM talk Kuznetsov conjectured that a maximal exceptional sequence is full if there exists at least one full exceptional sequence. In this research project we wish to investigate this conjecture on smooth projective toric varieties of Picard rank 3 via "combinatorial games''. Furthermore, we want to establish a constructive classification scheme for full exceptional sequences.

• DFG Programme: Research Grants