Compact subvarieties with ample normal bundles, algebraicity and cones of cycles

TL;DR

This paper investigates the properties of subvarieties with ample normal bundles in compact Kähler and projective manifolds, focusing on algebraic dimension and the position of curve classes within the Mori cone.

Contribution

It provides new results on the algebraicity of manifolds and the placement of curves with ample normal bundles inside the Mori cone.

Findings

Algebraic dimension constraints for subvarieties with ample normal bundles.

Curves with ample normal bundles lie in the interior of the Mori cone in various cases.

Abstract

In this note we study two features of submanifolds (subvarieties) with ample normal bundles in a compact K\"ahler manifold X. First, we study how algebraic X can be, i.e. we investigate the algebraic dimension. Second, we study curves with ample normal bundles in case X is projective. We prove in various cases that the class of the curve is in the interior of the Mori cone.