Special Lagrangian submanifolds with isolated conical singularities. III. Desingularization, the unobstructed case
| 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 third in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302356, 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 two papers math.DG/0211294, math.DG/0211295 studied the regularity of X near its singular points, and the moduli space of deformations of X. In this paper and the fourth math.DG/0302356 we 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. Suppose L_1,...,L_n are Asymptotically Conical SL m-folds in C^m, with L_i asymptotic to the cone C_i at infinity. We shrink L_i by a small 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 when t is sufficiently small we can deform N^t to a compact, nonsingular SL m-fold \tilde N^t via a small Hamiltonian deformation. This \tilde N^t depends smoothly on t, and as t --> 0 it converges to the singular SL m-fold X, in the sense of currents. This paper studies the simpler cases, where by topological conditions on X and L_i we avoid various obstructions to existence of \tilde N^t. The sequel math.DG/0302356 will consider more complex cases when these obstructions are nontrivial, and also desingularization in families of almost Calabi-Yau m-folds. | |
| dc.description | 54 pages. (v2) new reference, changed notation | |
| dc.identifier | https://arxiv.org/abs/math/0302355 | |
| dc.identifier | http://arxiv.org/abs/math/0302355 | |
| dc.identifier | Annals of Global Analysis and Geometry 26 (2004), 1-58. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66656 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Special Lagrangian submanifolds with isolated conical singularities. III. Desingularization, the unobstructed case | |
| dc.type | text |