English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove two gluing theorems for special Lagrangian (SL) conifolds in ℂ  m  . Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi–Yau manifolds.  In particular, our theorems yield the first examples of smooth SL conifolds with three or more planar ends and the first (non‐trivial) examples of SL conifolds which have a conical singularity (CS) but are not, globally, cones. We also obtain: (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 CSs with non‐compact asymptotically conical (AC) ends; (iii) a proof that there is no upper bound on the number of AC ends of an SL conifold and (iv) the possibility of replacing a given collection of CSs with a completely different collection of CSs and of AC ends.  As a corollary of (i), we improve a result by Arezzo and Pacard ( Comm. Pure Appl. Math.  56 (2003) 283–327) concerning minimal desingularizations of certain configurations of SL planes in ℂ  m  , intersecting transversally.

Special Lagrangian conifolds, II: gluing constructions in ℂ m