Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Author "Birkar, Caucher"
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Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs
Birkar, Caucher; Zhang, De-Qi (SpringerPublications mathématiques de l'IHÉS, 2016-01-18)For every smooth complex projective variety W of dimension d and nonnegative Kodaira dimension, we show the existence of a universal constant m depending only on d and two natural invariants of the very general fibres of ...
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Existence of Mori fibre spaces for 3-folds in char p
Birkar, Caucher; Waldron, J (ElsevierAdvances in Mathematics, 2017-06-20)We prove the following results for projective klt pairs of dimension 3 over an algebraically closed field of characteristic $p$>5: the cone theorem, the base point free theorem, the contraction theorem, finiteness of minimal ...
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The augmented base locus of real divisors over arbitrary fields
Birkar, Caucher (SpringerMathematische Annalen, 2016-07-08)We show that the augmented base locus coincides with the exceptional locus (i.e., null locus) for any nef $\Bbb R$-Cartier divisor on any scheme projective over a field (of any characteristic). Next we prove a semi-ampleness ...