Birational rigidity of quartic three-folds with a double point of rank 3

2024/10/19 by Pukhlikov, Aleksandr V. · 3 citations
#14E05 #14E07 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.15193

Abstract

We prove that a general three-dimensional quartic V in the complex projective space \mathbb P⁴, the only singularity of which is a double point of rank 3, is a birationally rigid variety. Its group of birational self-maps is, up to the finite subgroup of biregular automorphisms, a free product of 25 cyclic groups of order 2. It follows that the complement to the set of birationally rigid factorial quartics with terminal singularities is of codimension at least 3 in the natural parameter space.

Cited by

• Factoriality and birational rigidity of two families of singular quartic three-folds
• Local inequalities for cA_k singularities
• A survey on birational Rigidity of threefold Weighted Complete Intersections

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