Special Lagrangian submanifolds with isolated conical singularities. IV. Desingularization, obstructions and families
| dc.creator | Joyce, Dominic | |
| dc.date | 2003-02-28 | |
| dc.date | 2003-03-21 | |
| dc.date.accessioned | 2026-07-07T04:55:39Z | |
| dc.date.available | 2026-07-07T04:55:39Z | |
| dc.description | This is the fourth in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0303272 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m with isolated singularities at 0. Readers are advised to begin with the final paper math.DG/0303272 which surveys the series, gives examples, and applies the results to prove some conjectures. The first paper math.DG/0211294 studied the regularity of X near its singular points, and the second math.DG/0211295 the moduli space of deformations of X. The third paper math.DG/0302355 and this one construct desingularizations of X, realizing X as a limit of a family of compact, nonsingular SL m-folds \tilde N^t in M for small t>0. Let L_1,...,L_n be Asymptotically Conical SL m-folds in C^m, with L_i asymptotic to C_i at infinity. We shrink L_i by t>0, and glue tL_i into X at x_i for i=1,...,n to get a 1-parameter family of compact, nonsingular Lagrangian m-folds N^t for small t>0. Then we show using analysis that for small t we can deform N^t to a compact, nonsingular SL m-fold \tilde N^t via a small Hamiltonian deformation. As t --> 0 this \tilde N^t converges to X, in the sense of currents. The third paper math.DG/0302355 studied simpler cases, where by topological conditions on X and L_i we avoid obstructions to existence of \tilde N^t. This paper considers more complex cases when these obstructions are nontrivial, and also desingularization in smooth families of almost Calabi-Yau m-folds M^s for s in F, rather than a single almost Calabi-Yau m-fold M. | |
| dc.description | 54 pages. (v2) New reference, changed notation | |
| dc.identifier | https://arxiv.org/abs/math/0302356 | |
| dc.identifier | http://arxiv.org/abs/math/0302356 | |
| dc.identifier | Annals of Global Analysis and Geometry 26 (2004), 117-174. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66657 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Special Lagrangian submanifolds with isolated conical singularities. IV. Desingularization, obstructions and families | |
| dc.type | text |