D-Branes on C^3_6 part I: prepotential and GW-invariants

TL;DR

This paper explores brane configurations on noncompact Calabi-Yau manifolds derived from C^3/Z_6, using local mirror symmetry to compute GW-invariants and partially verify Hosono's conjecture.

Contribution

It applies local mirror symmetry to determine the prepotential for C^3/Z_6 resolutions, providing partial confirmation of Hosono's conjecture on GW-invariants.

Findings

Prepotential encodes GW-invariants except for certain null intersection curves.

Results partially confirm Hosono's conjecture.

Provides detailed analysis of brane configurations on noncompact Calabi-Yau manifolds.

Abstract

This is the first of a set of papers having the aim to provide a detailed description of brane configurations on a family of noncompact threedimensional Calabi-Yau manifolds. The starting point is the singular manifold C^3/Z_6, which admits five distinct crepant resolutions. Here we apply local mirror symmetry to partially determine the prepotential encoding the GW-invariants of the resolved varieties. It results that such prepotential provides all numbers but the ones corresponding to curves having null intersection with the compact divisor. This is realized by means of a conjecture, due to S. Hosono, so that our results provide a check confirming at least in part the conjecture.