dc.contributor.advisor Harris, Joseph D. dc.contributor.author Woolf, Matthew Jacob dc.date.accessioned 2014-06-06T16:52:12Z dc.date.issued 2014-06-06 dc.date.submitted 2014 dc.identifier.citation Woolf, Matthew Jacob. 2014. Relative Jacobians of Linear Systems. Doctoral dissertation, Harvard University. en_US dc.identifier.other http://dissertations.umi.com/gsas.harvard:11522 en dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274184 dc.description.abstract Let X be a smooth projective variety. Given any basepoint-free linear system, |D|, there is a dense open subset parametrizing smooth divisors, and over that subset, we can consider the relative Picard variety of the universal divisor, which parametrizes pairs of a smooth divisor in the linear system and a line bundle on that divisor. In the case where X is a surface, there is a natural compactification of the relative Picard variety, given by taking the moduli space of pure one-dimensional Gieseker-semistable sheaves with respect to some polarization. In the case of the projective plane, this is an irreducible projective variety of Picard number 2. We study the nef and effective cones of these moduli spaces, and talk about the relation with variation of Bridgeland stability conditions. en_US dc.description.sponsorship Mathematics en_US dc.language.iso en_US en_US dash.license LAA dc.subject Mathematics en_US dc.title Relative Jacobians of Linear Systems en_US dc.type Thesis or Dissertation en_US dash.depositing.author Woolf, Matthew Jacob dc.date.available 2014-06-06T16:52:12Z thesis.degree.date 2014 en_US thesis.degree.discipline Mathematics en_US thesis.degree.grantor Harvard University en_US thesis.degree.level doctoral en_US thesis.degree.name Ph.D. en_US dc.contributor.committeeMember Gaitsgory, Dennis en_US dc.contributor.committeeMember Chen, Dawei en_US dash.contributor.affiliated Woolf, Matthew Jacob
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