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Metric properties of spaces of stability conditions

Thursday 12th May 2011 - 15:30 to 16:30
INI Seminar Room 1
The space of Bridgeland stability conditions Stab(X) on the derived category D(X) of a variety X has a natural metric with respect to which the actions of the complex numbers C and of the automorphisms Aut(D(X)) of the category are isometries. Under mild assumptions this metric is complete. For example, when X is a complex projective curve with genus >0 one can compute directly that the quotient Stab(X)/C is isometric to the hyperbolic plane. I will discuss these results and some elementary consequences.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons