Special Lagrangian submanifolds with isolated conical singularities. II. Moduli spaces
This is the second in a series of five papers math.DG/0211294, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying 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 wit...
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| Format: | Journal article |
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2002
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| author | Joyce, D |
| author_facet | Joyce, D |
| author_sort | Joyce, D |
| collection | OXFORD |
| description | This is the second in a series of five papers math.DG/0211294, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying 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 proves some conjectures. In this paper we study the deformation theory of compact SL m-folds X in M with conical singularities. We define the moduli space M_X of deformations of X in M, and construct a natural topology on it. Then we show that M_X is locally homeomorphic to the zeroes of a smooth map \Phi : I --> O between finite-dimensional vector spaces. Here the infinitesimal deformation space I depends only on the topology of X, and the obstruction space O only on the cones C_1,...,C_n at x_1,...,x_n. If the cones C_i are "stable" then O is zero and M_X is a smooth manifold. We also extend our results to families of almost Calabi-Yau structures on M. The first paper math.DG/0211294 laid the foundations for the series, and studied the regularity of X near its singular points. The third and fourth papers math.DG/0302355, math.DG/0302356 construct desingularizations of X, realizing X as the limit of a family N^t of compact, nonsingular SL m-folds in M. |
| first_indexed | 2024-03-07T03:10:03Z |
| format | Journal article |
| id | oxford-uuid:b3e29233-e57d-47c2-ad9e-56aeed7ae9e9 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:10:03Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:b3e29233-e57d-47c2-ad9e-56aeed7ae9e92022-03-27T04:22:18ZSpecial Lagrangian submanifolds with isolated conical singularities. II. Moduli spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b3e29233-e57d-47c2-ad9e-56aeed7ae9e9Symplectic Elements at Oxford2002Joyce, DThis is the second in a series of five papers math.DG/0211294, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying 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 proves some conjectures. In this paper we study the deformation theory of compact SL m-folds X in M with conical singularities. We define the moduli space M_X of deformations of X in M, and construct a natural topology on it. Then we show that M_X is locally homeomorphic to the zeroes of a smooth map \Phi : I --> O between finite-dimensional vector spaces. Here the infinitesimal deformation space I depends only on the topology of X, and the obstruction space O only on the cones C_1,...,C_n at x_1,...,x_n. If the cones C_i are "stable" then O is zero and M_X is a smooth manifold. We also extend our results to families of almost Calabi-Yau structures on M. The first paper math.DG/0211294 laid the foundations for the series, and studied the regularity of X near its singular points. The third and fourth papers math.DG/0302355, math.DG/0302356 construct desingularizations of X, realizing X as the limit of a family N^t of compact, nonsingular SL m-folds in M. |
| spellingShingle | Joyce, D Special Lagrangian submanifolds with isolated conical singularities. II. Moduli spaces |
| title | Special Lagrangian submanifolds with isolated conical singularities. II.
Moduli spaces |
| title_full | Special Lagrangian submanifolds with isolated conical singularities. II.
Moduli spaces |
| title_fullStr | Special Lagrangian submanifolds with isolated conical singularities. II.
Moduli spaces |
| title_full_unstemmed | Special Lagrangian submanifolds with isolated conical singularities. II.
Moduli spaces |
| title_short | Special Lagrangian submanifolds with isolated conical singularities. II.
Moduli spaces |
| title_sort | special lagrangian submanifolds with isolated conical singularities ii moduli spaces |
| work_keys_str_mv | AT joyced speciallagrangiansubmanifoldswithisolatedconicalsingularitiesiimodulispaces |