May 26, 2008. Prof. James Carlson (Clay Institute, Harvard, USA). New results on cubic surfaces and cubic threefolds: hyperbolic structures on their moduli spaces.

The moduli space of cubic is modeled on the Poincare disk — complex hyperbolic space of dimension one — modulo a well understood group of symmetries. We show that the same is true of cubic surfaces and cubic threefolds. We discuss also related results for real cubic surfaces and the volume of their moduli space.

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