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arXiv · 1401.8050

Birational Geometry of the Space of Complete Quadrics

César Lozano Huerta
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Abstract

We study the birational geometry of the moduli space of complete $n$-quadrics $X$. We exhibit generators for Eff$(X)$ and Nef$(X)$, the cone of effective divisors and the cone of nef divisors, respectively. As a corollary X is a Mori Dream space. Furthermore, we run the MMP on $X$ and find a moduli interpretation for the models induced by the generators of the nef cone. In the case of complete quadric surfaces, we describe all the birational models of $X$ induced by the movable cone and find a moduli interpretation for some of these models.

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César Lozano Huerta. 2015-01-29. Birational Geometry of the Space of Complete Quadrics. https://arxiv.org/abs/1401.8050

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