Konstantinos C. Zygalakis (Edinburgh)
Title T.B.A.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Aliaksandra Novik (Imperial College)
Derived category of coherent systems on curves and its stability conditions abstract
Abstract:
Bridgeland stability conditions on derived categories have become a powerful tool for extracting geometric information about an underlying variety via wall-crossing phenomena. For a smooth irreducible complex projective curve C of genus greater than 0, Macrì showed that the space of stability conditions on D^b(C) is trivial up to the action of the universal covering of GL⁺(2, R). As a result, there is no room to deform stability conditions and apply wall-crossing.In this talk, we present one way to resolve this issue by enlarging the category from coherent sheaves on a curve to coherent systems. We introduce the derived category of coherent systems, describe an open subset of its stability manifold, and show that it detects the Brill–Noether theory of the underlying curve. This is based on joint work with Soheyla Feyzbakhsh.
14:00 • EPF Lausanne, CM 1 517