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On the canonical degrees of curves in varieties of general type
Language
en
Article de revue
This item was published in
Geometric And Functional Analysis. 2012, vol. 22, n° 5, p. 1051-1061
Springer Verlag
English Abstract
A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general ...Read more >
A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety.Read less <
Origin
Hal imported