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Automorphisms of the Quot schemes associated to compact Riemann surfaces

Indranil Biswas
(Tata Institute of Fundamental Research (TIFR), Mumbai)
Seminar
Torsdag, 6 august, 2015, at 16:30-17:30, in Aud. D2 (1531-119)
Abstrakt:
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.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen