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dc.contributor.advisorBayer, Arend
dc.contributor.advisorMaciocia, Antony
dc.contributor.authorTramel, Rebecca
dc.date.accessioned2017-03-15T11:41:23Z
dc.date.available2017-03-15T11:41:23Z
dc.date.issued2016-06-29
dc.identifier.urihttp://hdl.handle.net/1842/20990
dc.description.abstractLet 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.en
dc.language.isoenen
dc.publisherThe University of Edinburghen
dc.subjectCastelnuovo-type inequalityen
dc.subjectalgebraic geometryen
dc.subjectBridgeland stabilityen
dc.titleNew stability conditions on surfaces and new Castelnuovo-type inequalities for curves on complete-intersection surfacesen
dc.typeThesis or Dissertationen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD Doctor of Philosophyen


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