Characterizations of Projective Hulls by Analytic Discs

TL;DR

This paper characterizes the projective hull of compact sets in complex projective space using Poletsky sequences of analytic discs, extending known descriptions of holomorphic and plurisubharmonic hulls.

Contribution

It introduces a new description of the projective hull via analytic discs, linking it to Poletsky sequences and expanding the understanding of hulls in complex geometry.

Findings

Characterization of the projective hull using Poletsky sequences

Extension of known hull descriptions to projective space

New tools for studying complex hulls

Abstract

The notion of the projective hull of a compact set in a complex projective space was introduced by Harvey and Lawson in 2006. In this paper we describe the projective hull by Poletsky sequences of analytic discs, in analogy to the known descriptions of the holomorphic and the plurisubharmonic hull.