Geometry of the moduli space of genus zero curves

Diane Maclagan (University of Warwick)

G.205, Alan Turing Building,

The moduli space \(\overline{M}_{0,n}\) of stable genus zero curves with n marked points is a beautiful space that has been intensively studied by algebraic geometers and topologists for over half a century.  It arises from a simple geometric question ("How can we arrange n points on a sphere?"), but is the first nontrivial case of several interesting families of varieties (higher genus curves, stable maps, ...) and phenomena.  Despite the long history there are
still many mysteries about this variety.  I will introduce this moduli space, and discuss some combinatorial approaches to understanding it.

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