What question did this study set out to answer?

This work aims to develop a theoretical framework for two-valued algebraic group structures on the complex projective line and plane.

February 11, 2026

Algebraic 2-valued group structures on P¹, Kontsevich-type polynomials, and multiplication formulas. I

Puntos clave

This work aims to develop a theoretical framework for two-valued algebraic group structures on the complex projective line and plane.
Developed algebraic group structures depending on the choice of neutral element
Introduced local multiplication laws based on Buchstaber and Kontsevich polynomials
Constructed a new type of two-valued algebraic group structure on C
Provided a simple construction for a two-valued algebraic group structure on C
Demonstrated various multiplication laws using associated polynomials
Established connections between algebraic structures and complex projective geometry

Resumen

The theory of a 2-valued algebraic group structure on a complex plane and complex projective line is developed. In this theory, depending on the choice of the neutral element, the local multiplication law is given by the Buchstaber polynomial or the generalized Kontsevich polynomial. One of the most exciting results of the first part of our work is a simple construction of a 2-valued algebraic group structure on C different from well known coset-construction.

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Cite This Study

Krichever et al. (Thu,) studied this question.

synapsesocial.com/papers/698c1d1d267fb587c655faf6 https://doi.org/https://doi.org/10.4213/im9691e

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