# Degenerations of nilpotent associative commutative algebras

## TL;DR

This paper provides a comprehensive classification of how complex 5-dimensional nilpotent associative commutative algebras can degenerate into each other, enhancing understanding of their structural relationships.

## Contribution

It offers the first complete description of degenerations for 5-dimensional nilpotent associative commutative algebras, filling a gap in algebraic degeneration theory.

## Key findings

- Complete classification of degenerations among these algebras
- Identification of key degeneration pathways and invariants
- Structural insights into algebraic degeneration processes

## Abstract

We give a complete description of degenerations of complex $5$-dimensional nilpotent associative commutative algebras.