Schottky-Landau type theorem for holomorphic mappings (Q2828632)

\textit{P. A. Griffiths} [Ann. Math. (2) 93, 439--458 (1971; Zbl 0214.48601)] and \textit{K. Kodaira} [J. Differ. Geom. 6, 33--46 (1971; Zbl 0227.32008)] have obtained Schottky-Landau type theorems for holomorphic mappings \(f:B(r)\to V\), where \(B(r)=\{z\in\mathbb{C}^n:\|z\|<r\}\) and \(V\) is a smooth complete canonical algebraic variety, or a smooth projective algebraic variety of dimension \(n\) of general type. \textit{J. Carlson} and \textit{P. Griffiths} [Ann. Math. (2) 95, 557--584 (1972; Zbl 0248.32018)], and \textit{P. Griffiths} and \textit{J. King} [Acta Math. 130, 145--220 (1973; Zbl 0258.32009)] studied the case of non-compact target space. Their results imply the existence of an upper bound \(R_0\) such that \(f\) is defined on \(B(r)\) under some conditions for every \(r\leq R_0\).NEWLINENEWLINEIn the paper under review, by applying Kodaira's method together with Griffiths' singular modular form, the authors obtain a Carlson-Griffiths-King type theorem with a detailed form of the upper bound.