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The topology of terminal quartic 3-folds 10.17863/CAM.16206 Kaloghiros, Anne-Sophie Let 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. University of Cambridge 2007-06-20 Thesis Doctoral Doctor of Philosophy (PhD) en http://www.dspace.cam.ac.uk/handle/1810/214794 https://www.repository.cam.ac.uk/handle/1810/214794 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/193c0dd0-4e25-4958-b2d5-353dcfc44d51/download a9b761936dc7513fe747b59d107d6ded https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/53b32db4-2f07-4b20-8ffd-7bceb09c7b3f/download 0c9c10eeac6b4f2a41fb15f6ce3624e4 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/85809bde-2bd7-4229-bbfc-ee2d1306bd4b/download e57e2836d5359c01e8b643b7a91ed314 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2483ef06-584b-4053-ba19-a8b9265f41ad/download ac9819a76115e5d08f75dcc27ece3c08 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/4868d8b0-95e7-4d62-9842-c6de5ade4323/download 6844b66ba03b51c217df6bf890fe1ce5 https://www.rioxx.net/licenses/all-rights-reserved/ Algebraic Geometry Birational Geometry