Log Minimal Model Program for the Kontsevich Space of Stable Maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$

Details Log Minimal Model Program for the Kontsevich Space of Stable Maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$ Log Minimal Model Program for the Kontsevich Space of Stable Maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$

2007-09-04

arxiv.org/abs/0709.0438v1

Mathematics

Algebraic Geometry

13 pages, 3 figures, comments are welcome

Scientific paper

This work is inspired by conversations with Izzet Coskun and Joe Harris. We run the log minimal model program for the Kontsevich space of stable maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$ and give modular interpretations to all the intermediate spaces appearing in the process. In particular, we show that one component of the Hilbert scheme $\mathcal H_{3,0,3}$ is the flip of $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$ over the Chow variety. Finally as an easy corollary we obtain that $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$ is a Mori dream space.

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