Orbifolds, special varieties and classification theory

Campana, Frédéric

doi:10.5802/aif.2027

Cited by 183 publications

(291 citation statements)

References 3 publications

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“…This conjecture comes from Campana's theory of "special" variety (cf. [4]). A complex manifold X which admits a holomorphic map f : C → X with metrically dense image has vanishing Kobayashi pseudo-metric.…”

Section: Resultsmentioning

confidence: 99%

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On fundamental groups of algebraic varieties and value distribution theory

Yamanoi¹

2010

Ann. inst. Fourier

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Section: Resultsmentioning

confidence: 99%

“…[4, Conjecture 9.2]), and that the fundamental group of a "special" variety would be almost abelian (cf. [4,Conjecture 7.1]). For more discussion about Conjecture 1.2, we refer the reader to [4].…”

Section: Resultsmentioning

confidence: 99%

On fundamental groups of algebraic varieties and value distribution theory

Yamanoi¹

2010

Ann. inst. Fourier

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“…C D/ jX z to the general fiber of f is klt (if .K X C / is not big we actually add a small ample to it). Then, supposing for simplicity that X and Y are smooth, and f regular, we invoke Campana's positivity result [Ca3], Theorem 4.13, to deduce that f .K X =Z C C D/ Q K Z is weakly positive. Then by results contained in [MM], [BDPP] and [N] the variety Z is forced to be either uniruled or to have zero Kodaira dimension.…”

Section: Again Notice That If X Is As In the Examplementioning

confidence: 99%

Rational connectedness modulo the non-nef locus

Broustet¹,

Pacienza²

2011

Comment. Math. Helv.

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Abstract. It is well known that a smooth projective Fano variety is rationally connected. Recently Zhang [Z2] (and later Hacon and McKernan [HM] as a special case of their work on the Shokurov RC-conjecture) proved that the same conclusion holds for a klt pair .X; / such that .K X C / is big and nef. We prove here a natural generalization of the above result by dropping the nefness assumption. Namely we show that a klt pair .X; / such that .K X C/ is big is rationally connected modulo the non-nef locus of .K X C /. This result is a consequence of a more general structure theorem for arbitrary pairs .X; / with .K X C / pseff. Mathematics Subject Classification (2010). 14J40.

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“…On the other hand, potential density fails for curves and for certain classes of higherdimensional varieties with K X positive, by a theorem of Faltings. We refer the reader to [5] for a general discussion of the connections between classification theory and potential density questions.…”

Section: Introductionmentioning

confidence: 99%