Mori's program for the Kontsevich moduli space
Dawei Chen, Harvard

We run Mori's program for the Kontsevich space of stable maps $ \overline{\mathcal M}_{0,0}(\mathbb P^{3},3)$ and give geometric interpretations of all the intermediate spaces. In particular, we show that one component of the corresponding Hilbert scheme is the flip of $\overline{\mathcal M}_{0,0}(\mathbb P^{3},3)$ over the Chow variety. If time allows, more examples will be presented to illustrate what we should expect in general. This is part of an ongoing project joint with Izzet Coskun.