Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces

Author: Joyce Dominic  

Publisher: Springer Publishing Company

ISSN: 0232-704X

Source: Annals of Global Analysis and Geometry, Vol.25, Iss.4, 2004-06, pp. : 301-352

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

This is the second in a series of five papers studying special Lagrangian submanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds M with singularities X1, …, Xn locally modelled on special Lagrangian cones C1, …, Cn in \mathbb CM with isolated singularities at 0. Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL M-folds X in M with conical singularities. We define the moduli space \mathcal mX of deformations of X in M, and construct a natural topology on it. Then we show that \mathcal mX is locally homeomorphic to the zeroes of a smooth map Φ: \mathcal iX\mathcal oX between finite-dimensional vector spaces.Here the infinitesimal deformation space \mathcal iX depends only on the topology of X, and the obstruction space \mathcal oX only on the cones C1, …, Cn at X1, …, Xn. If the cones Ci are stable then \mathcal oX is zero, and \mathcal mX is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M.