Moduli space of complexes of vector bundles over Gorenstein Calabi-Yau curves


The moduli stack of complexes of vector bundles over a Gorenstein Calabi-Yau curve, considered up to chain isomorphisms, admits a 0-shifted Poisson structure in the sense of Calaque-Pantev-Toen-Vaquie-Vezzosi. We will give several classical examples of Poisson varieties appearing in representation theory and integrable system, that are naturally Poisson substacks of the above mentioned stack. Using derive algebraic geometry, we are able to prove some new results on these Poisson varieties. This is a joint work with Alexander Polishchuk.