Algebraic $2$-valued group structures on $\mathbb P^1$, Kontsevich-type polynomials, and multiplication formulas. I

Victor Matveevich Buchstaber; Ilia Yurievich Gaiur; Vladimir Nikolaevich Rubtsov

doi:10.4213/im9691

Algebraic $2$-valued group structures on $\mathbb P^1$, Kontsevich-type polynomials, and multiplication formulas. I

Известия Российской академии наук Серия математическая 2026

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Authors: Victor Matveevich Buchstaber, Ilia Yurievich Gaiur, Vladimir Nikolaevich Rubtsov

DOI: 10.4213/im9691

Cited by: 1

References: 24

Abstract

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 $\mathbb C$ different from well known coset-construction.

Fields of Study & Subjects

Polynomial and algebraic computation Algebraic Geometry and Number Theory Advanced Combinatorial Mathematics

Publication details

Journal / source: Известия Российской академии наук Серия математическая
Publisher: Steklov Mathematical Institute
Volume: 90
Issue: 1
Pages: 37–72
Publication date: 1 January 2026
Language: RU

References 24