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Smooth projective stacks : ample bundles and D-affinity
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El Haloui, Karim (2018) Smooth projective stacks : ample bundles and D-affinity. PhD thesis, University of Warwick.
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WRAP_Theses_El_Haloui_2018.pdf - Submitted Version - Requires a PDF viewer. Download (1054Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3226884~S15
Abstract
This thesis is on the study of sheaves of O-modules and D-modules on projective stacks. In chapter 1, a historical perspective is given on the main fidings that have shaped and influenced the study carried out and exposed in this thesis. In chapter 2, the principal definitions and results used in the forthcoming sections are recalled. An appendix is added at the end of this chapter exposing self-containedly why quotient singularities and orbifolds are two equivalent notions. In chapter 3, the property of ampleness of vector bundles on projective stacks is generalised and studied. Basic properties are given; in particular it is proved that weighted projective stacks have ample tangent vector bundle. In chapter 4, D-modules on projective stacks are studied. General conditions on the weights and the shift guaranteeing a weighted projective stack to be D-affine are given. Thus, proving a version of the Beilinson-Bernstein Localisation Theorem. In particular, a weighted projective stack is D-affine if and only if the greatest common divisor of its weights is one. A theorem of Kashiwara is extended to smooth projective stacks, it is shown that the category of D-modules on a smooth closed projective substack [X] is equivalent to the category of D-modules on the ambient smooth projective stack [Y ] supported on [X].
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Geometry, Algebraic, Algebraic stacks, Geometry, Projective, Sheaf theory, Vector bundles, Geometry, Affine | ||||
| Official Date: | May 2018 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Rumynin, Dmitriy, 1971- | ||||
| Format of File: | |||||
| Extent: | vii, 108 leaves | ||||
| Language: | eng |
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