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arXiv · 2512.22091

Factoriality and birational rigidity of two families of singular quartic three-folds

Aleksandr V. Pukhlikov
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Abstract

In this paper we study two families of three-dimensional quartics in the complex projective space ${\mathbb P}^4$: hypersurfaces with a unique quadratic singularity of rank 3, which is resolved by two blowups, and hypersurfaces with two quadratic singularities of rank 3 and 4, respectively. Both families have codimension 3 in the natural parameter space. For a Zariski general quartic in each of these families we prove factoriality and birational rigidity and describe its group of birational self-maps.

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Aleksandr V. Pukhlikov. 2025-12-26. Factoriality and birational rigidity of two families of singular quartic three-folds. https://arxiv.org/abs/2512.22091

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