University of Sydney Algebra Seminar

Svetlana Makarova

Friday 28 February, 12-1pm, in Carslaw 175

Vector bundles on stacky curves

There is a well-known theory of moduli of vector bundles on curves. Analogous construction for stacky curves turns out to be subtler: for example, the naïvely defined slope no longer gives bounded semistable locus. In this talk, I will speak about an alternative way of defining semistability, prove algebraicity of the moduli stack of vector bundles and boundedness of its semistable locus, and use the rapidly developing theory of Beyond GIT to show that the semistable locus admits a good moduli space. This work is joint with Chiara Damiolini, Vicky Hoskins and Lisanne Taams.
This talk is preceded by the talk at Macquarie University on Wednesday 26.02 at 2 pm. There, I will focus on Grothendieck duality for derived algebraic stacks, which is an extension of the theory that we needed to study properties of determinantal line bundles on moduli of bundles on stacky curves.