Displaying similar documents to “The Mukai conjecture for log Fano manifolds”

Orbifolds, special varieties and classification theory

Frédéric Campana (2004)

Annales de l’institut Fourier

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This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected...

On del Pezzo fibrations

Massimiliano Mella (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Subsheaves of the cotangent bundle

Paolo Cascini (2006)

Open Mathematics

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For any smooth projective variety, we study a birational invariant, defined by Campana which depends on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We provide new bounds for a related invariant in any dimension and in particular we show that it is equal to the Kodaira dimension of the variety, in dimension up to 4, if this is not negative.

On log canonical divisors that are log quasi-numerically positive

Shigetaka Fukuda (2004)

Open Mathematics

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Let (X Δ) be a four-dimensional log variety that is projective over the field of complex numbers. Assume that (X, Δ) is not Kawamata log terminal (klt) but divisorial log terminal (dlt). First we introduce the notion of “log quasi-numerically positive”, by relaxing that of “numerically positive”. Next we prove that, if the log canonical divisorK X+Δ is log quasi-numerically positive on (X, Δ) then it is semi-ample.

Pluricanonical maps for threefolds of general type

Gueorgui Tomov Todorov (2007)

Annales de l’institut Fourier

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In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.