Polynomial hull of a torus fibered over the circle

TL;DR

This paper investigates the polynomial hull of a specific 2-sheeted torus over the circle, showing it consists of holomorphic discs and describing the boundary structure when non-degenerate.

Contribution

It proves that the polynomial hull of a 2-sheeted torus with winding number 1 is a union of holomorphic discs and characterizes the boundary as a Levi-flat solid torus.

Findings

Polynomial hull is a union of holomorphic discs

Boundary of non-degenerate hull is Levi-flat and foliated by discs

Results apply to tori with winding number 1

Abstract

Given a 2-sheeted torus over the circle with winding number 1, we prove that its polynomial hull is a union of 2-sheeted holomorphic discs. Moreover when the hull is non degenerate its boundary is a Levi-flat solid torus foliated by such discs.