On the extendability of projective varieties: a survey

TL;DR

This survey explores the rich geometric theory behind extending projective varieties as hyperplane sections of larger varieties, highlighting key concepts and open problems in the field.

Contribution

It provides a comprehensive overview of the current state of research on the extendability of projective varieties, summarizing known results and identifying future directions.

Findings

Summarizes key results on extendability conditions.

Highlights open problems and conjectures.

Connects geometric intuition with algebraic conditions.

Abstract

We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.