Colloquium abstracts

Arusha C
TIFR
January 6, 2022

Poincare and Picard bundles for moduli spaces of vector bundles over nodal curves:  Poincare and Picard bundles and their different variants have been a topic of interest ever since the quest for moduli spaces of vector bundles was initiated, owing to their universality. Though a great deal is known about these objects in the case of smooth curves, the study on singular curves has been relatively slow. Interestingly, the results for irreducible nodal curves are very similar to those for smooth curves; however,the proofs are different and difficult. It was known for a long time that there does not exist a Poincare bundle for the moduli problem of vector bundles on smooth curves if the rank and degree are not coprime. We primarily aim to discuss the non-existence of a Poincare bundle parametrised by the moduli space of vector bundles on nodal curves when the rank and degree are not coprime. There has also been a considerable amount of interest to understand the stability of Poincare and projective Poincare bundles as well as Picard and projective Picard bundles.Th