Spectral Curves for Almost-Complex Tori in $ S ^6 $

TL;DR

This paper introduces spectral curves associated with almost-complex tori in the 6-sphere, analyzing their algebraic and geometric properties to understand the moduli space of such immersions.

Contribution

It constructs spectral curves for almost-complex tori in S^6 and computes the dimension of their moduli space, providing new insights into their geometric structure.

Findings

Spectral curves are generically smooth.

The dimension of the moduli space is explicitly computed.

Eigenline bundles lie in a well-defined moduli space.

Abstract

To each non-isotropic almost-complex immersion of a 2-torus into $ S ^ 6 $ we associate an algebraic curve, called the spectral curve, and a linear flow in the intersection of two Prym varieties on this spectral curve. We show that generically the spectral curve is smooth and compute the dimension of the moduli space of such curves and of the torus in which the eigenline bundles lie.