## Differential equations on hypersurfaces in $$\mathbb P^4$$. (Equations différentielles sur les hypersurfaces de $$\mathbb P^4$$.)(French)Zbl 1115.14009

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 [G. Dethloff and 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.

### MSC:

 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14J70 Hypersurfaces and algebraic geometry 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds

Zbl 0982.32022
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### References:

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