Moduli space and deformations of special Lagrangian submanifolds with edge singularities

TL;DR

This paper investigates the deformation space of special Lagrangian submanifolds with edge singularities in Calabi-Yau manifolds, using elliptic theory to describe its local structure and smoothness conditions.

Contribution

It introduces a framework applying elliptic theory to analyze the moduli space of special Lagrangian submanifolds with edge singularities, providing conditions for smoothness.

Findings

The moduli space's local structure is characterized by a general theorem.

When the obstruction space vanishes, the moduli space is a smooth finite-dimensional manifold.

The approach extends elliptic theory to singular geometric settings.

Abstract

Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this paper we use elliptic theory for edge-degenerate differential operators on singular manifolds to study the moduli space of deformations of special Lagrangian submanifolds with edge singularities. We obtain a general theorem describing the local structure of the moduli space. When the obstruction space vanishes the moduli space is a smooth, finite dimensional manifold.