Special Lagrangian conifolds, I: Moduli spaces (extended version)
Abstract
This is the extended version of the paper "Special Lagrangian conifolds, I: Moduli spaces", which discusses the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds. The conifold category allows for the simultaneous presence of conical singularities and of non-compact, asymptotically conical, ends. Our main theorem is the natural next step in the chain of results initiated by McLean and continued by the author and Joyce. We survey all these results, providing a unified framework for studying the various cases and emphasizing analogies and differences. Compared to "Special Lagrangian conifolds, I", this paper contains more detail but the same results. The paper also lays down the geometric foundations for our paper "Special Lagrangian conifolds, II: Gluing constructions in C^m".
Cite
@article{arxiv.1211.2800,
title = {Special Lagrangian conifolds, I: Moduli spaces (extended version)},
author = {Tommaso Pacini},
journal= {arXiv preprint arXiv:1211.2800},
year = {2012}
}
Comments
This paper will not be submitted for publication. It is the extended version of a paper with the same title arXiv:1002.1222 , to appear in Proc. LMS. The additional details in this version may be of interest to some readers