TL;DR
This paper interprets the construction of toric systems associated with exceptional sequences on toric weak Fano surfaces as an instance of mirror symmetry, extending the duality to a broader class of surfaces.
Contribution
It introduces a mirror symmetry perspective to toric systems and extends the duality to all toric weak Fano surfaces with cyclic full strongly exceptional sequences.
Findings
Establishes a mirror symmetry interpretation of toric systems.
Extends duality to all toric weak Fano surfaces with exceptional sequences.
Provides a new framework connecting toric geometry and mirror symmetry.
Abstract
Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak Fano surface a toric system, which defines a new toric surface. In this note we interprete this construction as an instance of mirror symmetry and extend it to a duality on the set toric weak Fano surfaces equiped with a cyclic full strongly exceptional sequence.
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