Z-linear Gale duality and poly weighted spaces (PWS)

TL;DR

This paper explores Gale duality through Z-linear algebra, identifying poly weighted spaces as a new class of Q-factorial complete toric varieties with torsion-free class groups, generalizing weighted projective spaces.

Contribution

It introduces poly weighted spaces (PWS) as a novel class of toric varieties characterized via Z-linear Gale duality, extending the concept of weighted projective spaces.

Findings

Poly weighted spaces have torsion-free class groups.

Gale duality can be understood through Z-linear algebra.

PWS generalize weighted projective spaces.

Abstract

The present paper is devoted to discussing Gale duality from the Z-linear algebraic point of view. This allows us to isolate the class of Q-factorial complete toric varieties whose class group is torsion free, here called poly weighted spaces (PWS), as an interesting generalization of weighted projective spaces (WPS).