Toric structures in derived categories and representations of algebras

• Applicant: Privatdozent Dr. Markus Perling
• Subject Area: Mathematics
• Term: from 2009 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 125767185

In this project we want to study relations between algebraic geometry and the representation theory of algebras via tilting theory. The most important aspects we want to investigate are, on the one hand, the construction of so-called exceptional sequences on algebraic varieties, in particular on rational surfaces. On the other hand, for the higher-dimensional case we want to consider relations between tilting theory and birational transforms. A particular role here is played by a paper in superstring theory by Herbst, Hori, and page (2008). The part of this article which is relevant for this project is concerned with the generalization of Landau-Ginzburg models to the multigraded case; in this context, also local aspects of tilting are being investigated. In this project we want to work out and further investigate the mathematical content of these results.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory