Asymptotic period relations for Jacobian elliptic surfaces

TL;DR

This paper provides an asymptotic description of the period locus for simply connected Jacobian elliptic surfaces and hyperelliptic curves, revealing a surprising connection to the alkanes of organic chemistry.

Contribution

It introduces a novel asymptotic framework linking the period loci of elliptic surfaces and hyperelliptic curves with chemical structures.

Findings

Period locus described asymptotically for elliptic surfaces and hyperelliptic curves

The descriptions are essentially identical

Connection to alkanes in organic chemistry

Abstract

We find an asymptotic description of the period locus of simply connected Jacobian elliptic surfaces and of the period locus of hyperelliptic curves. The two descriptions are essentially the same, and are given by the alkanes of organic chemistry.