A generalization of twistor lines for complex tori

TL;DR

This paper extends the concept of twistor lines in the period domain of complex tori by introducing new non-compact analytic curves, analyzing their properties, and exploring their role in the connectivity of the domain.

Contribution

It introduces two new types of curves in the period domain, generalizing classical twistor lines and studying their geometric and topological properties.

Findings

New non-compact analytic curves are introduced in the period domain.

The curves' compactifications preserve certain cohomology classes.

One type of curve ensures twistor path connectivity of the domain.

Abstract

In this work we generalize the classical notion of a (compact) twistor line in the period domain of compact complex tori. We introduce two new types of lines, which are non-compact analytic curves in the period domain of complex tori. We study the analytic properties of the compactifications of the curves, the preservation of cohomology classes of type (1,1) along the curves and the twistor path connectivity of the period domain by the curves of one of the new types.