On the normalized local volume of a non-closed point

TL;DR

This paper demonstrates that the normalized local volume of a non-closed point can be represented using the normalized local volumes of closed points, linking local geometric invariants.

Contribution

It introduces a method to express the normalized local volume of non-closed points through those of closed points, providing a new perspective on local volume calculations.

Findings

Normalized local volume of non-closed points can be expressed via closed points.

Provides a new formula linking local volumes of different types of points.

Enhances understanding of local volume invariants in algebraic geometry.

Abstract

In this note, we show that the normalized local volume of a non-closed point can be expressed in terms of the normalized local volumes of closed points.