2015/02/09 by Jean Vallès, Vallès, Jean · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #math.AT
paper · pdf · doi:10.48550/arxiv.1502.02416
openalex publication_date 2015/02/09 · arxiv created 2016/01/12 · arxiv updated 2016/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A plane curve on a the projective space over a field of characteristic zero is free if its associated sheaf T of tangent vector fields tangent is a free module. Relatively few free curves are known. Here we prove that a divisor consisting of a union of curves of a pencil of plane projective curves with the same degree and with a smooth base locus is a free divisor if and only this union contains all the singular members of the pencil and its Jacobian ideal is locally a complete intersection.