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On the logarithmic Kobayashi conjecture
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14. November 2007
We study the hyperbolicity of the log variety (ℙn,X), where X is a very general hypersurface of degree d ≧ 2n + 1 (which is the bound predicted by the Kobayashi conjecture). Using a positivity result for the sheaf of (twisted) logarithmic vector fields, which may be of independent interest, we show that any log-subvariety of (ℙn, X) is of log-general type, give a new proof of the algebraic hyperbolicity of (ℙn, X), and exclude the existence of maximal rank families of entire curves in the complement of the universal degree d hypersurface. Moreover, we prove that, as in the compact case, the algebraic hyperbolicity of a log-variety is a necessary condition for the metric one.
Received: 2006-03-30
Revised: 2006-09-26
Published Online: 2007-11-14
Published in Print: 2007-10-26
© Walter de Gruyter
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- Perfect powers from products of terms in Lucas sequences
- Multiple recurrence and convergence for sequences related to the prime numbers
- Transfinite diameter and the resultant
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Artikel in diesem Heft
- Uniform bounds for two variable real oscillatory integrals and singularities of mappings
- On the first and second variations of a nonlocal isoperimetric problem
- Perfect powers from products of terms in Lucas sequences
- Multiple recurrence and convergence for sequences related to the prime numbers
- Transfinite diameter and the resultant
- Rational computations of the topological K-theory of classifying spaces of discrete groups
- On a question of Igusa III: A generalized Poisson formula for pairs of polynomials
- On the logarithmic Kobayashi conjecture
