Blow-ups of weighted projective planes at a point: Exploring the parameter space of triangles and the MDS property

Javier González Anaya, University of California at Riverside

We discuss the Mori dream space (MDS) property for blow-ups of toric surfaces defined by rational plane triangles at a general point. We consider a parameter space of all such triangles and show how it can be used to prove the MDS property for these varieties. Furthermore, this parameter space helps explain most known results in the area and has also led to surprising new results, including examples of such surfaces with a semi-open effective cone. This is joint work with José Luis González and Kalle Karu.

MC 5403