A polynomial invariant for plane curve complements: Krammer polynomials

2017/07/18 by Aktas, Mehmet Emin, Cellat, Serdar, Gurdogan, Hubeyb
#14H30 #14H45 (Secondary) #20F36 (Primary) #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.05585

Abstract

We use the Krammer representation of the braid group in Libgober's invariant and construct a new multivariate polynomial invariant for curve complements: Krammer polynomial. We show that the Krammer polynomial of an essential braid is equal to zero. We also compute the Krammer polynomials of some certain n-gonal curves.

Related

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• Braid Monodromy of Special Curve
• Braid Group techniques in Complex Geometry V: The fundamental group of the complement of a Veronese generic projection
• Numerical computation of braid groups