The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content



Fibrations on the moduli of parabolic connections on P^1 minus 4 points

Simpson, C (Nice Sophia Antipolis)
Friday 18 March 2011, 11:30-12:30



This reports on joint work with Frank Loray and Masa-Hiko Saito. Given a connection with parabolic structure, one can look at the limit as $t\rightarrow 0$ in Hitchin's twistor space. The limit is a $C^*$-fixed Higgs bundle. Breaking up the moduli space according to the isomorphism class of the limit leads to a decomposition in locally closed subvarieties. In the case of rank $2$ connections on $P^1-\{ t_1,t_2,t_3,t_4\}$ we are able to show that the subvarieties are closed. They are the fibers of fibrations, depending on the parabolic weights, which are already known: appearing for example in work of Arinkin and Lysenko, and of Iwasaki, Inaba, Saito. Katz's middle convolution is one of Okamoto's symmetries exchanging the different types of fibrations.

Back to top ∧