Mirror fibrations and root stacks of weighted projective spaces

TL;DR

This paper reveals a natural connection between the orbifold Chow ring of root stacks over weighted projective spaces and Jacobian algebras of functions on singular varieties, enhancing understanding of their algebraic structures.

Contribution

It introduces a novel perspective linking orbifold Chow rings of root stacks to Jacobian algebras via Ginzburg-Landau models for weighted projective spaces.

Findings

Orbifold Chow ring corresponds to Jacobian algebra of a specific function.

Partial compactification of Ginzburg-Landau model relates to the algebraic structure.

Provides a new framework for studying weighted projective spaces and their stacks.

Abstract

We show that the orbifold Chow ring of a root stack over a well-formed weighted projective space can be naturally seen as the Jacobian algebra of a function on a singular variety given by a partial compactification of its Ginzburg-Landau model.