Seminar in Real and Complex Geometry

Thursday, June 19, 2025, 16:15-17:45, online via zoom




Marco Golla
(Uppsala University)

Alexander polynomials and symplectic curves in CP^2


Abstract
             
Libgober defined the Alexander polynomial of a (complex) plane projective curve and showed that it detects some Zariski pairs of curves: these are curves with the same degree and the same singularities but with non-homeomorphic complements. He also proved that the Alexander polynomial of a curve divides the Alexander polynomial of its link at infinity and the product of Alexander polynomials of the links of its singularities. We extend Libgober's definition to the symplectic case and prove that the divisibility relations also hold in this context. This is joint work with Hanine Awada.