Abstract:A general linear determinantal quartic in $\mathbb{P}^4$ is nodal, non-$\mathbb{Q}$-factorial and rational. We show that the family $\mathcal{F}$ of such quartics also contains rational $\mathbb{Q}$-factorial quartics, and that a generic member of $\mathcal{F}$ can specialize to a rational non-$\mathbb{Q}$-factorial double quadric. We prove that the birational geometry of these three types of 3-folds is governed by the extrinsic geometry of a curve $C\subset \mathbb{P}^3$ of degree 10 and genus 11.
From: Manuel Leal [view email]
[v1]
Sun, 20 Apr 2025 02:47:05 UTC (278 KB)
[v2]
Sun, 24 Aug 2025 16:32:08 UTC (280 KB)
[v3]
Fri, 12 Jun 2026 17:27:16 UTC (378 KB)
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