Neighborhoods of subvarieties in homogeneous spaces

TL;DR

This paper investigates the complex function theory and fundamental groups of neighborhoods around compact subvarieties in homogeneous spaces, extending previous results to cases beyond ample normal bundles.

Contribution

It broadens the understanding of neighborhoods of subvarieties in homogeneous spaces by analyzing their holomorphic and meromorphic functions and fundamental groups, building on prior work.

Findings

Extended results to non-ample normal bundle cases

Characterized the function theory of neighborhoods in homogeneous spaces

Analyzed the fundamental groups of these neighborhoods

Abstract

We study the holomorphic/meromorphic function theory and the fundamental group of Euclidean open neighborhoods of compact subvarieties in homogeneous spaces; building on results of Hironaka, Hartshorne, Napier and Ramachandran in the ample normal bundle case.