# A combinatorial proof of the smoothness of catalecticant schemes associated to complete intersections

## TL;DR

This paper provides a combinatorial proof demonstrating the smoothness of catalecticant schemes associated with zero-dimensional complete intersections having equal degree generators, enhancing understanding of their geometric properties.

## Contribution

It introduces a combinatorial approach to prove the smoothness of catalecticant schemes for a specific class of complete intersections, which was previously unestablished.

## Key findings

- Proof of smoothness along an open subset of an irreducible component
- Establishment of combinatorial methods in algebraic geometry
- Insights into the structure of catalecticant schemes

## Abstract

For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, we give a combinatorial proof of the smoothness of the corresponding catalecticant schemes along an open subset of a particular irreducible component.