Syzygies and cohomology (A08)

• Subject Area: Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286237555

Syzygies play an important role in computational algebraic geometry. They form a cornerstone for basic algorithms and constructions. For example, the computation of coherent sheaf cohomology on projective varieties is based on syzygy computations over exterior algebras via the theory of Tate resolutions. In this project we plan to advance the concept of syzygies further, both from a theoretical and from a computer algebra point of view. Goals are an algorithm to compute higher direct image complexes, improvement and parallelization of the basic syzygy algorithm and the investigation of asymptotics of syzygies.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 195: Symbolic Tools in Mathematics and their Application
• Applicant Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
• Project Head: Professor Dr. Frank-Olaf Schreyer