Christine von Renesse, University of Massachusetts, Amherst

Combinatorial descriptions of the Mori cone of a toric variety

The Mori cone of a toric variety can be computed by using the codimension-one cones (walls) of the corresponding fan. Reid's results show that in the complete simplicial case you can instead use so called primitive collections to find generators of the Mori cone. I will review this and then show how to generalize it to any toric variety with convex support. We will then look at examples of non-simplicial fans and some of their simplicial refinements to see if and how we can use the generators of the Mori cone of the refinements for the original fans.

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