Higher Chow cycles on Jacobian of Fermat curves and Hypergeometric functions

2017/03/30 by Subham Sarkar, Sarkar, Subham
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1703.10370

Abstract

In this paper we construct certain higher Chow cycles in the K₁ of the Jacobian of Fermat curves, generalising a construction of Collino. We further compute the regulator of these elements in terms of special values of hypergeometric functions. Otsubo has computed the regulator of certain elements of K₀ and K₂ of Fermat varieties and this paper is along the same lines.

Related

• Indecomposable Higher Chow cycles on Jacobians
• Note on curves in a Jacobian
• Indecomposable Higher Chow Cycles on Low Dimensional Jacobians
• Construction of Higher Chow cycles on cyclic coverings of ℙ¹ × ℙ¹
• Regulator of the Hesse cubic curves and hypergeometric functions