Chow Forms, Chow Quotients and Quivers with Superpotential

TL;DR

This paper links toric Calabi-Yau singularities with quivers with superpotential, providing a new method to compute Chow forms and the principal A-determinant, bridging algebraic geometry and physics.

Contribution

It introduces a novel approach to derive Chow forms from quivers with superpotential for CY3 singularities, connecting geometric and physical theories.

Findings

Chow forms can be derived from quivers with superpotential.

A new method for computing the principal A-determinant is established.

The work bridges algebraic geometry with the AdS/CFT correspondence.

Abstract

We consider 3-dimensional toric Calabi-Yau singularities which arise as cones over the Chow quotient for a torus acting on projective space. We show that the Chow forms of the closures of the codimension 2 orbits can very easily be written down from the quiver with superpotential which corresponds with the given CY3 singularity under the correspondence between CY3 singularities and quivers with superpotential which is part of the AdS/CFT correspondence in physics. We also prove that this provides a new method for computing the principal A-determinant in the theory of Gelfand-Kapranov-Zelevinsky.