On Birational Transformations of Pairs in the Complex Plane
J\'er\'emy Blanc, Ivan Pan, Thierry Vust
TL;DR
This paper investigates birational transformations of the complex projective plane that preserve an algebraic curve, summarizing current knowledge and presenting new findings in this area.
Contribution
It offers a comprehensive overview of the field and introduces novel results on birational transformations maintaining algebraic curves.
Findings
New classifications of birational transformations
Extended understanding of invariant algebraic curves
Updated theoretical framework for transformations
Abstract
This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.
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