Special Lagrangian conifolds, I: Moduli spaces (extended version)

2012/11/12 by Tommaso Pacini, Pacini, Tommaso
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1211.2800

openalex publication_date 2012/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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".

Citations

• Symplectic manifolds and their lagrangian submanifolds
• Calibrated geometries

Related

• Special Lagrangian conifolds, II: gluing constructions in ℂ m
• Special Lagrangian submanifolds with isolated conical singularities. V. Survey and applications
• Lectures on special Lagrangian geometry
• Deformations of Asymptotically Conical Special Lagrangian Submanifolds
• Special Lagrangian submanifolds with isolated conical singularities. IV. Desingularization, obstructions and families