On dimension of poset variety

TL;DR

This paper calculates the dimension of the variety of subspace representations of a finite poset with a fixed dimension vector, linking it to the Euler quadratic form for geometric insight.

Contribution

It provides a formula for the dimension of poset representation varieties using the Euler quadratic form, offering a geometric interpretation.

Findings

Dimension expressed via Euler quadratic form

Provides geometric interpretation of the quadratic form

Advances understanding of poset representation varieties

Abstract

For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the Euler quadratic form associated with a partially ordered set, which gives a geometric interpretation of this form.