AINFINITY · Moduli spaces and derived categories
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2007-09-01 → 2009-08-31
- EU contribution
- €151,982
- Participants
- 1
- Scheme
- EIF
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Results in brief
Final Activity and Management Report Summary - AINFINITY (Moduli spaces and derived categories)
This project is on the interaction of algebra and geometry, more precisely representation theory of quivers and geometric invariant theory. The project studies varieties with group actions coming from two sources. One is automorphism groups of projective representations acting on homomorphism spaces, including varieties of complexes of projective modules. The second is varieties of A-infinity modules. Whenever possible, in view of applications, the researcher has concentrated on actions which are related to subjects outside representation theory of quivers, for example Lie theory and algebraic geometry. The main achievements are the existence of open orbits in actions of automorphism groups of projective representations with applications to questions about Richardson elements in Lie theory, and the existence of filtrations in derived module categories with tilting objects with dimension two.
Data: CORDIS, © European Union
Project objective
We propose a project on the interaction of algebra and geometry, more precisely representation theory of finite dimensional algebras and geometric invariant theory. The main objective is to study moduli spaces and stability conditions for derived categories of finite dimensional algebras.When studying families of objects in derived categories of finite dimensional algebras, there are two approaches, which have proven to be useful. One is the varieties of complexes of projective modules, and the another is varieties of A-infinity modules. Both of these approaches allows for explicitly described affined varieties, such that quasi-isomorphism classes in the derived category correspond to orbits under the action of an algebraic group. The researcher will use both these approaches. He will study stable and semi-stable complexes. He will also investigate the geometric properties of the obtained moduli spaces. In particular he will look for explicit descriptions of when they are smooth and projective, and when they give geometric quotients on stable complexes.An important aim of the project will be to explicitly study moduli problems in derived categories of important classes of algebras, for example canonical algebras and Koszul algebras. Whenever possible, in view of applications, the researcher will concentrate on classes of algebras which via equivalences, are related to derived categories from outside representation theory, for example algebraic geometry.
Original text from CORDIS.
Participants
- UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6 · PARISCoordinatorFrance
Links
Data: CORDIS, © European Union