Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712345
Title: New stability conditions on surfaces and new Castelnuovo-type inequalities for curves on complete-intersection surfaces
Author: Tramel, Rebecca
ISNI:       0000 0004 6063 1453
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2016
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Abstract:
Let X be a smooth complex projective variety. In 2002, [Bri07] defined a notion of stability for the objects in Db(X), the bounded derived category of coherent sheaves on X, which generalized the notion of slope stability for vector bundles on curves. There are many nice connections between stability conditions on X and the geometry of the variety. In 2012, [BMT14] gave a conjectural stability condition for threefolds. In the case that X is a complete intersection threefold, the existence of this stability condition would imply a Castelnuovo-type inequality for curves on X. I give a new Castelnuovo-type inequality for curves on complete intersection surfaces of high degree. I then show how this bound would imply the bound conjectured in [BMT14] if a weaker bound could be shown for curves of lower degree. I also construct new stability conditions for surfaces containing a curve C whose self-intersection is negative. I show that these stability conditions lie on a wall of the geometric chamber of Stab(X), the stability manifold of X. I then construct the moduli space Mσ (OX) of σ-semistable objects of class [OX] in K0(X) after wall-crossing.
Supervisor: Bayer, Arend ; Maciocia, Antony Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.712345  DOI: Not available
Keywords: Castelnuovo-type inequality ; algebraic geometry ; Bridgeland stability
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