Alejandra Vincente Colmenares, Department of Pure Mathematics, University of Waterloo
“Stable vector bundles over Riemann surfaces”
It is well-known (due to the so called jump phenomenon) that any moduli space of vector bundles over a Riemann surface cannot be Hausdorff. One way around this problem is to exclude the ”unstable” bundles and to identify semistable bundles under the notion of ”S-equivalence”. Indeed, in the 1960s, Mumford proved that the moduli space of S-equivalence classes of rank 2 semistable bundles of fixed degree over a Riemann surface is a complex projective variety. In this talk, we will discuss the notion of semistability (in the Mumford-Takemoto sense) and present some of its basic properties. All the necessary background will be introduced.