Addition-deletion for conic-line arrangements with split Chern polynomial

2025/10/03 by Măcinic, Anca, Vallès, Jean
#14B05 #14C17 #14F06 #14H50 (Primary) #14H60 #32S22 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.02771

Abstract

We present combinatorial/geometric obstructions induced by the factorization over the integers of the Chern polynomial of the bundle of logarithmic vector fields associated to a complex projective plane curve. Our results generalize at the same time similar results on projective lines arrangements whose characteristic polynomial factors over the integers and results on free curves. We give a splitting criterion for a rank 2 vector bundle, in terms of restrictions to smooth conics.

Citations

• Deletion-addition of a smooth conic for free curves
• Jacobian schemes of conic-line arrangements and eigenschemes
• Numerical invariants and moduli spaces for line arrangements
• Free divisors in a pencil of curves
• Roots of characteristic polynomials and intersection points of line arrangements
• The Module of Logarithmic p-forms of a Locally Free Arrangement

Related

• Arrangements of curves and algebraic surfaces
• On Poincaré polynomials for plane curves with quasi-homogeneous singularities
• Deletion-addition of a smooth conic for free curves
• On plus-one generated conic-line arrangements with simple singularities
• Arrangements of rational sections over curves and the varieties they define