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

Friday 18th March 2011 - 11:30 to 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.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons