Seminar by Indranil Biswas (TIFR, Mumbai)

Title: Automorphisms of the Quot schemes associated to compact Riemann surfaces

2015.08.03 | Jane Jamshidi

Date Thu 06 Aug
Time 16:30 17:30
Location Aud. D2 (1531-119)


Let $Q$ denote the Quot scheme that
parametrizes all the torsion quotients of ${\mathcal O}^{\oplus r}_X$ of degree $d$, where $X$ is a compact Riemann surface.
The group $\text{PGL}(r, {\mathbb C})$ acts
faithfully on $Q$ via the standard action of $\text{GL}(r, {\mathbb C})$ on
${\mathcal O}^{\oplus r}_X$. We prove that $\text{PGL}(r,
{\mathbb C})$ is the connected component, containing the identity element, of $\text{Aut}(Q)$. As an application,
we prove that the isomorphism class of $Q$ uniquely
determines the isomorphism class of the Riemann surface $X$.
This is a joint work with A. Dhillon and J. Hurtubise.