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On the classification of orbifold del Pezzo surfaces
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Cuzzucoli, Alice (2020) On the classification of orbifold del Pezzo surfaces. PhD thesis, University of Warwick.
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WRAP_Theses_Cuzzucoli_2020.pdf - Submitted Version - Requires a PDF viewer. Download (1183Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3467781~S15
Abstract
Chapter 1 is devoted to outlining the problem. We introduce the background material, namely define orbifold del Pezzo surfaces, qG_deformations and graded ring methods. Following this, we use the properties of these classes of surfaces to compute numerical invariants and find a bound for the number of singularities. Ultimately, we obtain a list of numerical candidates for our surfaces.
In Chapter 2 we recall some aspects of the Mori theory for surfaces, we define the notion of minimal surfaces and we find surfaces with singularity content (n; k1_1 5(1; 2)+k2_1 3(1; 1)) having Picard rank _ = 1. Later we establish a Directed Minimal Model Program for our class of surfaces and by analysing our numerical candidates we find the isomorphism classes of our del Pezzo surfaces.
In Chapter 3 we discuss the toric case: we find all of the possible mutation classes of our orbifolds and we introduce the formalism of T_varieties. We then show how to link qG_deformations to equivariant complexity 1 deformations. We give a couple of enlightening examples to better understand the complexity 1 environment and deformations.
In Chapter 4 we finally construct the cascades from the representatives of the qG_classes and we give a complete count of all the deformation classes for our type of surfaces.
Chapter 5 contains tables representing a summary of the MMP outcomes and the classification of toric surfaces representing the mutation classes.
Lastly, in the Appendix we report the calculations that lead us to the classification of the isomorphism classes in Chapter 2.
Item Type: | Thesis (PhD) | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Orbifolds, Surfaces, Graded rings | ||||||
Official Date: | 20 April 2020 | ||||||
Dates: |
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Institution: | University of Warwick | ||||||
Theses Department: | Mathematics Institute | ||||||
Thesis Type: | PhD | ||||||
Publication Status: | Unpublished | ||||||
Supervisor(s)/Advisor: | Reid, Miles (Miles A.) | ||||||
Format of File: | |||||||
Extent: | xiii, 130 leaves : illustrations | ||||||
Language: | eng |
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