Strong Franchetta Conjecture for Linear Systems

2014/02/10 by Matthew Woolf, Woolf, Matthew · 1 citation
Computer Science · Mathematics · #14C20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Codimension #Conjecture #FOS: Mathematics #Mathematics #Polynomial and algebraic computation #Projective variety #Pure mathematics #Statistics #Tensor decomposition and applications #Variety (cybernetics) #math.AG #msc:14C20

paper · pdf · doi:10.48550/arxiv.1402.2128

published in arXiv (Cornell University) (Cornell University) · 7 pages; comments welcome

arxiv created 2014/02/10 · openalex publication_date 2014/02/10 · arxiv updated 2014/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study rational sections of the relative Picard variety of a linear system on a smooth projective variety. Specifically, we prove that if the linear system is basepoint-free and the locus of non-integral divisors has codimension at least two, then all rational sections of the relative Picard variety come from restrictions of line bundles on the variety.

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• Monodromy and vanishing cycles for sufficiently ample linear systems on simply connected surfaces

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