The Ruled Vertex and D-E Degenerations

TL;DR

This paper computes genus topological amplitudes on ruled surfaces from D-E singularities in Calabi-Yau threefolds, confirming the ruled vertex formalism and supporting mirror symmetry predictions.

Contribution

It introduces a method to compute topological amplitudes on ruled surfaces with D-E degenerations, validating the ruled vertex formalism.

Findings

Results agree with genus zero mirror symmetry calculations

Supports the validity of the ruled vertex formalism for degenerate torus actions

Provides comprehensive genus topological amplitude computations

Abstract

We compute all genus topological amplitudes on configurations of ruled surfaces obtained by resolving lines of D-E singularities in compact Calabi-Yau threefolds. We find that our results are in agreement with genus zero mirror symmetry calculations, which is further evidence for the ruled vertex formalism for degenerate torus actions.