On the extendability of projective varieties: a survey
Angelo Felice Lopez (with an appendix by Thomas Dedieu)

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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Tensor decomposition and applications
