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

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

2011-09-15

arxiv.org/abs/1109.3339v2

Mathematics

Differential Geometry

Prior version was a draft. This version, now complete, includes new section 5, new theorem 6.12 and several changes elsewhere.

Scientific paper

We prove a general gluing result for special Lagrangian (SL) conifolds in C^m. 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 C^m, intersecting transversally.

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