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<https://discovery.ucl.ac.uk/id/eprint/10196777> <http://purl.org/dc/terms/title> "Birational geometry of fibrations in positive characteristic: On the canonical bundle formula and the Iitaka conjectures"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10196777> <http://purl.org/ontology/bibo/abstract> "This thesis concerns the study of fibrations between algebraic varieties over fields\r\nof positive characteristic. These are fundamental objects used to study the classification\r\nof algebraic varieties. In particular, my thesis focuses on two problems: the\r\ncanonical bundle formula and the Iitaka conjectures.\r\nLet f : X \\to Z be a fibration between normal projective varieties over a perfect\r\nfield of positive characteristic.\r\nAssume the Minimal Model Program and the existence of log resolutions. Then,\r\nwe prove that, if K_X is f-nef, Z is a curve and the general fibre has nice singularities,\r\nthe moduli part is nef, up to a birational map. As a corollary, we prove nefness of\r\nthe moduli part in the K-trivial case. In particular, if X has dimension 3 and is\r\ndefined over a perfect field of characteristic p > 5, the canonical bundle formula\r\nholds unconditionally.\r\nWe also study an Iitaka-type inequality k(X,-K_X) \\leq k(X_z,-K_{X_z})+k(Z,-K_Z)\r\nfor the anticanonical divisors, where X_z is a general fibre of f. We conclude that\r\nit holds when X_z has good F-singularities. Furthermore, we give counterexamples\r\nin characteristics 2 and 3 for fibrations with non-normal fibres, constructed from\r\nTango–Raynaud surfaces."^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10196777> <http://purl.org/dc/terms/date> "2024-09-28" .
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