Real regulator maps with finite 0-locus
Abstract
Abstract A Laurent polynomial in two variables is tempered if its edge polynomials are cyclotomic. Variation of coefficients leads to a family of smooth complete genus- g curves carrying a canonical algebraic upper K 2 K 2 $K_2$ -class over a g -dimensional base S , hence to an extension of admissible variations of mixed Hodge structure (or normal function) on S . We prove that the double struck upper R R $\mathbb{R}$ -split locus of this extension is finite. Consequently, the torsion locus of the normal function and the A -factor locus for the family of curves are also finite.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
Amino Acid Enzymes and Metabolism
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Compositio Mathematica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 162
- Issue
- 6
- Pages
- 1256–1273
- Publication date
- 1 June 2026
- Language
- EN