A symplectic dynamics proof of the degree-genus formula
arXiv:1905.03054 · doi:10.1007/s40598-021-00195-7
Abstract
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.
24 pages, 11 figures