The Ruled Vertex and Nontoric del Pezzo Surfaces

TL;DR

This paper develops a method to compute the topological partition function for local nontoric del Pezzo surfaces using the ruled vertex formalism, expanding computational tools in algebraic geometry.

Contribution

It introduces a novel application of the ruled vertex formalism to nontoric del Pezzo surfaces, providing a new computational approach.

Findings

Successfully constructed the topological partition function for nontoric del Pezzo surfaces.

Extended the applicability of the ruled vertex formalism beyond toric cases.

Provided explicit calculations demonstrating the method's effectiveness.

Abstract

We construct the topological partition function of local nontoric del Pezzo surfaces using the ruled vertex formalism.