On two pencils of cubic curves

2016/06/15 by Pauline Bailet, Bailet, Pauline
Computer Science · Mathematics · #14DXX #14FXX #14H50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1606.04858

openalex publication_date 2016/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give two examples of plane curve arrangements of pencil type which are very close to line arrangements, though the action of the monodromy operator on the first cohomology group of the Milnor Fiber has eigenvalues of order 5 and 6, showing that surprising situations can occur for larger classes of curve arrangements than for line arrangements. Our computations rely on the algorithm given by A. Dimca and G. Sticlaru which detects the non trivial monodromy eigenspaces of free curves.

Citations

• Geometry of cohomology support loci for local systems I

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