Hyperbolicity of Nodal Hypersurfaces
نویسندگان
چکیده
We show that a nodal hypersurface X in P3 of degree d with a sufficiently large number l of nodes, l > 8 3 (d2 − 5 2 d), is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families.
منابع مشابه
Hyperbolicity of Hypersurfaces with Nodes
Kobayshi’s conjecture proposes that the general hypersurface X of P3 of degree ≥ 5 is hyperbolic. This paper shows that nodal hypersurfaces X with many nodes are algebraically quasi-hyperbolic, i.e. there are only finitely many rational and elliptic curves on X. A key element is the existence of many symmetric log-differentials in the minimal resolution of the nodal hypersurface.
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