2017/10/25 by Adrien Dubouloz, Takashi Kishimoto, Dubouloz, Adrien +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1710.09108
openalex publication_date 2017/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An algebraic variety is called \mathbbA1-cylindrical if it contains an \mathbbA1-cylinder, i.e. a Zariski open subset of the form Z×\mathbbA1 for some algebraic variety Z. We show that the generic fiber of a family f:X→ S of normal \mathbbA1-cylindrical varieties becomes \mathbbA1-cylindrical after a finite extension of the base. Our second result is a criterion for existence of an \mathbbA1-cylinder in X which we derive from a careful inspection of a relative Minimal Model Program ran from a suitable smooth relative projective model of X over S.