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dc.contributor.advisorHarris, Joseph D.
dc.contributor.authorDeopurkar, Anand
dc.date.accessioned2012-12-19T21:44:46Z
dc.date.issued2012-12-19
dc.date.submitted2012
dc.identifier.citationDeopurkar, Anand. 2012. Alternate Compactifications of Hurwitz Spaces. Doctoral dissertation, Harvard University.en_US
dc.identifier.otherhttp://dissertations.umi.com/gsas.harvard:10308en
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:10086270
dc.description.abstractWe construct several modular compactifications of the Hurwitz space \(H^d_{g/h}\) of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. They are obtained by allowing the branch points of the cover to collide to a variable extent, generalizing the spaces of twisted admissible covers of Abramovich, Corti, and Vistoli. The resulting spaces are very well-behaved if d is small or if relatively few collisions are allowed. In particular, for d = 2 and 3, they are always well-behaved. For d = 2, we recover the spaces of hyperelliptic curves of Fedorchuk. For d = 3, we obtain new birational models of the space of triple covers. We describe in detail the birational geometry of the spaces of triple covers of \(P^1\) with a marked fiber. In this case, we obtain a sequence of birational models that begins with the space of marked (twisted) admissible covers and proceeds through the following transformations: (1) sequential contractions of the boundary divisors, (2) contraction of the hyperelliptic divisor, (3) sequential flips of the higher Maroni loci, (4) contraction of the Maroni divisor (for even g). The sequence culminates in a Fano variety in the case of even g, which we describe explicitly, and a variety fibered over \(P^1\) with Fano fibers in the case of odd g.en_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dash.licenseLAA
dc.subjectHurwitz spaceen_US
dc.subjectMaronien_US
dc.subjectmathematicsen_US
dc.subjectbirational geometryen_US
dc.subjecttrigonal curveen_US
dc.subjectmoduli spaceen_US
dc.titleAlternate Compactifications of Hurwitz Spacesen_US
dc.typeThesis or Dissertationen_US
dc.date.available2012-12-19T21:44:46Z
thesis.degree.date2012en_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorHarvard Universityen_US
thesis.degree.leveldoctoralen_US
thesis.degree.namePh.D.en_US
dc.contributor.committeeMemberHarris, Josephen_US
dc.contributor.committeeMemberMazur, Barryen_US
dc.contributor.committeeMemberVakil, Ravien_US


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