On the canonical module of Toric Surfaces in $P^4$

TL;DR

This paper proves that the canonical module of any toric surface embedded in projective 4-space is always Cohen-Macaulay, highlighting a key algebraic property of such surfaces.

Contribution

It establishes a universal Cohen-Macaulay property of the canonical module for toric surfaces in P^4, a result not previously known.

Findings

Canonical module of toric surfaces in P^4 is Cohen-Macaulay

Provides a new understanding of algebraic properties of toric surfaces

Enhances classification of toric varieties in algebraic geometry

Abstract

Our main result states that for a toric surface in $P^4$ canonical module is always Cohen-Macaulay.