Limits of tangent spaces along a subvariety at an isolated singularity

TL;DR

This paper investigates the behavior of tangent spaces approaching an isolated singularity along a subvariety, revealing that the set of limit tangent spaces has a dimension one less than the subvariety.

Contribution

It establishes a precise relationship between the dimension of the subvariety and the set of limit tangent spaces at an isolated singularity.

Findings

The dimension of limit tangent spaces is one less than the subvariety's dimension.

Provides a geometric characterization of tangent space limits at singularities.

Enhances understanding of singularity structure in algebraic geometry.

Abstract

We show that the dimension of the set of limits of tangent spaces along a subvariety at an irreducible isolated singularity is one less than the dimension of the subvariety itself.