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

Aleksandr V. Pukhlikov

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arXiv · 2410.15193

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

Aleksandr V. Pukhlikov

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Abstract

We prove that a general three-dimensional quartic $V$ in the complex projective space ${\mathbb P}^4$, 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.

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Aleksandr V. Pukhlikov. 2024-10-19. Birational rigidity of quartic three-folds with a double point of rank 3. https://arxiv.org/abs/2410.15193

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