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dc.contributor.authorKaloghiros, Anne-Sophie
dc.date.accessioned2009-03-02T09:37:57Z
dc.date.available2009-03-02T09:37:57Z
dc.date.issued2007-06-20
dc.identifier.otherPhD.30695
dc.identifier.urihttp://www.dspace.cam.ac.uk/handle/1810/214794
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/214794
dc.description.abstractLet Y be a quartic hypersurface in P^4 with terminal singularities. The Grothendieck-Lefschetz theorem states that any Cartier divisor on Y is the restriction of a Cartier divisor on P^4 . However, no such result holds for the group of Weil divisors. More generally, let Y be a terminal Gorenstein Fano 3-fold with Picard rank 1. Denote by s(Y )=h_4 (Y )-h^2 (Y ) = h_4 (Y )-1 the defect of Y. A variety is Q-factorial when every Weil divisor is Q-Cartier. The defect of Y is non-zero precisely when the Fano 3-fold Y is not Q-factorial. Very little is known about the topology of non Q-factorial terminal Gorenstein Fano 3-folds. Q-factoriality is a subtle topological property: it depends both on the analytic type and on the position of the singularities of Y . In this thesis, I endeavour to answer some basic questions related to this global topolgical property. First, I determine a bound on the defect of terminal quartic 3-folds and on the defect of terminal Gorenstein Fano 3-folds that do not contain a plane. Then, I state a geometric motivation of Q-factoriality. More precisely, given a non Q-factorial quartic 3-fold Y , Y contains a special surface, that is a Weil non-Cartier divisor on Y . I show that the degree of this special surface is bounded, and give a precise list of the possible surfaces. This question has traditionally been studied in the context of Mixed Hodge Theory. I have tackled it from the point of view of Mori theory. I use birational geometric methods to obtain these results.en
dc.language.isoenen
dc.subjectAlgebraic Geometryen
dc.subjectBirational Geometryen
dc.titleThe topology of terminal quartic 3-foldsen
dc.typeThesisen
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.identifier.doi10.17863/CAM.16206


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