A note related to Severi's finiteness theorem

TL;DR

This paper explores a high-dimensional extension of Severi's finiteness theorem, providing a constructive proof using algebraic geometry of surfaces to address a related question.

Contribution

It introduces a high-dimensional generalization of Severi's finiteness theorem and offers a constructive proof leveraging algebraic geometry techniques.

Findings

Established a high-dimensional analogue of Severi's finiteness theorem

Provided a constructive proof using algebraic geometry of surfaces

Addressed a related open question in algebraic geometry

Abstract

In this note we consider a question related to the high-dimensional generalization of the classical Severi's finiteness theorem for curves. We will introduce some background and then state the main result. The proof of the main result is constructive and we mainly use algebraic geometry of surfaces.