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Title: Application of Bridgeland stability to the geometry of abelian surfaces
Author: Alagal, Wafa Abdullah
ISNI:       0000 0004 6059 5552
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2016
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A key property of projective varieties is the very ampleness of line bundles as this provides embeddings into projective space and allows us to express the variety in equational terms. In this thesis we study the general version of this property which is k- very ampleness of line bundles. We introduce the notation of critical k-very ampleness and compute it for abelian surfaces. The property of k-very ampleness is usually discussed using tools from divisor theory but we take a different approach and use methods from derived algebraic geometry as part of program to use properties of the derived category of a variety to access the geometry of the variety. In particular, we use the Fourier-Mukai transform, moduli spaces of sheaves and properties of Bridgeland stability. We compute walls for certain Bridgeland stable spaces and certain Chern characters and to complete the picture we study the moduli spaces of torsion sheaves with minimal first Chern class and we go on to compute the walls for these as well building on tools developed earlier in the thesis.
Supervisor: Maciocia, Antony ; Hering, Milena Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: ample ; very ample ; line bundle ; abelian surface ; stable sheaf ; moduli space ; Bridgeland’s stability condition