### Metric properties of spaces of stability conditions

**Woolf, J ***(Liverpool)*

Thursday 12 May 2011, 15:30-16:30

Seminar Room 1, Newton Institute

#### Abstract

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.