Oka and Alexander polynomials of symplectic curves and divisibility relations

TL;DR

This paper proves divisibility relations for Oka and Alexander polynomials of symplectic curves in the complex projective plane, providing new proofs for algebraic curves and exploring their topological properties.

Contribution

It establishes new divisibility relations for symplectic curves' polynomials and offers alternative proofs for algebraic curves' Alexander polynomial divisibility.

Findings

Proved Libgober's divisibility relations for symplectic curves

Provided new proofs for divisibility relations in algebraic curves

Enhanced understanding of topological invariants of symplectic and algebraic curves

Abstract

We prove Libgober's divisibility relations for Oka and Alexander polynomials of symplectic curves in the complex projective plane. Along the way, we give new proofs of the divisibility relations for the Alexander polynomials of complex algebraic curves with respect to a generic line at infinity.