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The second main theorem for holomorphic curves into semiabelian varieties. II. (English) Zbl 1145.32009

Summary: We establish the second main theorem with the best truncation level one
\[ T(r;\omega_{\bar Z,J_k(f)})\leq N_1(r;J_k(f)^*Z)+\varepsilon T_f(r)\|_\varepsilon \]
for the \(k\)-jet lift \(J_k(f):\mathbb C\to J_k(A)\) of an algebraically non-degenerate entire holomorphic curve \(f:\mathbb C\to A\) into a semi-abelian variety \(A\) and an arbitrary algebraic reduced subvariety \(Z\) of \(J_k(A)\); the low truncation level is important for applications. Finally, we give some applications, including the solution of a problem posed by Mark Green (1974).
[For part I of this paper see the authors, Acta Math. 188, 129–161 (2002; Zbl 1013.32010).]

MSC:

32H30 Value distribution theory in higher dimensions

Citations:

Zbl 1013.32010
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References:

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