Geometry of linear determinantal quartic 3-folds via their intermediate Jacobian

2025/04/20 by Leal, Manuel, Huerta, César Lozano, Vite, Montserrat
#14E05 (Primary) 14E07 #14E08 #14E30 #14H45 #14H50 #14J30 #14M06 #14M12 #14M20 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.14461

Abstract

A general linear determinantal quartic in ℙ⁴ is nodal, non-ℚ-factorial and rational. We show that the family F of such quartics also contains rational ℚ-factorial quartics, and that a generic member of F can specialize to a rational non-ℚ-factorial double quadric. We describe the birational geometry of these three types of 3-folds, showing that it is governed by the extrinsic geometry of a curve C⊂ ℙ³.

Related

• Non-rational nodal quartic threefolds
• Birational geometry of terminal quartic 3-folds II: the importance of beings Q-factorial
• Factoriality and birational rigidity of two families of singular quartic three-folds
• A classification of terminal quartic 3-folds and applications to rationality questions
• Q-factorial quartic threefolds