Nonrational del Pezzo fibrations

2004/07/20 by Ivan Cheltsov, Cheltsov, Ivan
Mathematics · #14E08 #14J30 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0407343

openalex publication_date 2004/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a general divisor in |3M+nL| on the rational scroll Proj(⊕_i=1⁴O_ℙ¹(d_i)), where d_i and n are integers, M is the tautological line bundle, L is a fibre of the natural projection to ℙ¹, and d₁\geqslant...\geqslant d₄=0. We prove that X is rational \iff d₁=0 and n=1.

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