Desingularization of Coassociative 4-folds with Conical Singularities: Obstructions and Applications
arXiv:1209.5116 · doi:10.1090/S0002-9947-2014-06193-X
Abstract
We study the problem of desingularizing coassociative conical singularities via gluing, allowing for topological and analytic obstructions, and discuss applications. This extends the author's earlier work on the unobstructed case. We interpret the analytic obstructions geometrically via the obstruction theory for deformations of conically singular coassociative 4-folds, and thus relate them to the stability of the singularities. We use our results to describe the relationship between moduli spaces of coassociative 4-folds with conical singularities and those of their desingularizations. We also apply our theory in examples, including to the known conically singular coassociative 4-folds in compact holonomy G_2 manifolds.
56 pages, v2: minor corrections and added comments, published version
References in corpus (6)
- Special Lagrangian cones with higher genus links
- Ruled Lagrangian Submanifolds of the 6-Sphere
- Deformation Theory of Asymptotically Conical Coassociative 4-folds
- Coassociative K3 fibrations of compact G_2-manifolds
- Special Lagrangian conifolds, II: Gluing constructions in C^m
- Coassociative cones that are ruled by 2-planes