Displaying similar documents to “Orbifolds, special varieties and classification theory”

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.

Compact quotients of large domains in complex projective space

Finnur Lárusson (1998)

Annales de l'institut Fourier

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We study compact complex manifolds covered by a domain in n -dimensional projective space whose complement E is non-empty with ( 2 n - 2 ) -dimensional Hausdorff measure zero. Such manifolds only exist for n ≥ 3 . They do not belong to the class 𝒞 , so they are neither Kähler nor Moishezon, their Kodaira dimension is - ∞ , their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds,...