Dense entire curves in Rationally Connected manifolds

Frederic Campana; Joerg Winkelmann

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arXiv · 1905.01104

Dense entire curves in Rationally Connected manifolds

Frederic Campana·Joerg Winkelmann

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Abstract

We show the existence of metrically dense entire curves in rationally connected complex projective manifolds confirming for this case a conjecture according to which such entire curves on projective manifolds exist if and only if these are "special". We also show that such a dense entire curve may be chosen in such a way that it does not lift to any of its ramified covers, answering in this case a question of Corvaja and Zannier about the Nevanlinna analog of the `weak Hilbert property' of arithmetic geometry. We consider briefly the other test case of the conjecture, namely manifolds with $c_1=0$. Furthermore we discuss entire curves in normal rational surfaces avoiding the singular locus.

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Frederic Campana, Joerg Winkelmann. 2019-05-03. Dense entire curves in Rationally Connected manifolds. https://arxiv.org/abs/1905.01104

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