Canonical and log canonical thresholds of multiple projective spaces

2019/06/27 by Pukhlikov, Aleksandr V.
#14E05 #14E07 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.11802

Abstract

In this paper we show that the global (log) canonical threshold of d-sheeted covers of the M-dimensional projective space of index 1, where d\geqslant 4, is equal to one for almost all families (except for a finite set). The varieties are assumed to have at most quadratic singularities, the rank of which is bounded from below, and to satisfy the regularity conditions. This implies birational rigidity of new large classes of Fano-Mori fibre spaces over a base, the dimension of which is bounded from above by a constant that depends (quadratically) on the dimension of the fibre only.

Related

• Bounds for log canonical thresholds with applications to birational rigidity
• Birationally rigid finite covers of the projective space
• Alpha invariants of birationally rigid Fano threefolds
• Noether-Fano Inequalities and Canonical Thresholds on Fano Varieties
• Singularities of linear systems and boundedness of Fano varieties