Differential equations on hypersurfaces in \(\mathbb P^4\).
Here the author proves that for all integers \(d \geq 97\) (resp. \(d \geq 92\)) and every smooth degree \(d\) hypersurface \(X \subset \mathbb {P}^4_{\mathbb {C}}\) every entire curve of \(X\) (resp. \(\mathbb {P}^4_{\mathbb {C}}\backslash X\)) satisfies an algebraic differential equation of degree \(3\). The main tool is the logarithmic version of Demailly vector bundle of differential jets [\textit{G. Dethloff} and \textit{S. Lu}, Osaka J. Math. 38, No. 1, 185--237 (2001; Zbl 0982.32022)]. Apart from this fundamental tool the main trick is to use the decomposition of the graded object obtained from the vector bundle of jets of order \(3\) into Schur's irreducible representations.
scientific article; zbMATH DE number 5125005
scientific article