Algebraic Geometry Seminar: The local projective plane, a fractal-like curve, and Gamma_1(3)
Speakers
Details
I will report on joint work with E. Macri on the space of stability conditions for the derived category of the total space of the canonical bundle on the projective plane. It is a 3–dimensional manifold, with many chamber decompositions coming from the behaviour of moduli spaces of stable objects under change of stability conditions.
I will explain how this space is related to classical results by Drezet and Le Potier on stable vector bundles on the projective plane. Using the space helps to determine the group of auto-equivalences, which includes a subgroup isomorphic to \Gamma_1(3). Finally, via mirror symmetry, it contains a universal cover of the moduli space of elliptic curves with \Gamma_1(3)–level structure.
I will explain how this space is related to classical results by Drezet and Le Potier on stable vector bundles on the projective plane. Using the space helps to determine the group of auto-equivalences, which includes a subgroup isomorphic to \Gamma_1(3). Finally, via mirror symmetry, it contains a universal cover of the moduli space of elliptic curves with \Gamma_1(3)–level structure.
