Birational Geometry of the Space of Complete Quadrics

2014/01/31 by Huerta, César Lozano
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.8050

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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