A symplectic dynamics proof of the degree-genus formula - Albers, Peter; Geiges, Hansjörg; Zehmisch, Kai (Arxiv, 2019)
We classify global surfaces of section for the Reeb flow of the standard contact form on the 3-sphere, defining the Hopf fibration. As an application, we prove the degree-genus formula for complex projective curves, using an elementary degeneration process inspired by the language of holomorphic buildings in symplectic field theory.
Gesehen am 12.07.2022