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arXiv · 1905.03054

A symplectic dynamics proof of the degree-genus formula

Peter Albers·Hansjörg Geiges·Kai Zehmisch
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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.

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Peter Albers, Hansjörg Geiges, Kai Zehmisch. 2019-05-08. A symplectic dynamics proof of the degree-genus formula. https://doi.org/10.1007/s40598-021-00195-7

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