Calculus of Variations and Geometric Measure Theory

T. Pacini

Special Lagrangian conifolds, II: Gluing constructions in C^m

created by pacini on 15 Sep 2011
modified on 21 Nov 2011



Inserted: 15 sep 2011
Last Updated: 21 nov 2011

Year: 2011


We prove a general gluing result for special Lagrangian (SL) conifolds in Cm. These conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds.

In particular, our result yields: (i) a desingularization procedure for transverse intersection and self-intersection points, using ``Lawlor necks''; (ii) a construction which completely desingularizes any SL conifold by replacing isolated conical singularities with non-compact asymptotically conical (AC) ends; (iii) a proof that there is no upper bound on the number of AC ends of a SL conifold; (iv) the possibility of replacing a given collection of conical singularities with a completely different collection of conical singularities and of AC ends.

As a corollary of (i) we improve a result by Arezzo and Pacard concerning minimal desingularizations of certain configurations of SL planes in Cm, intersecting transversally.