Katharina Heinrich: The Hilbert scheme of twisted cubics

One of the few Hilbert schemes that is well-understood is the moduli space of twisted cubics, that is smooth, proper, rational curves of degree 3 in IP^3. The explicit description was done by R. Piene and M. Schlessinger in 1985. I will explain some of their results, do some explicit calculations and, if time permits, explain how the Hilbert scheme is related to the space of Cohen-Macaulay curves that I work on.