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Erwan Rousseau

Publications and source records attributed to Erwan Rousseau.

40 records · Page 3Linked to original sources
arXiv2006

Equations differentielles sur les hypersurfaces de l'espace projectif complexe de dimension 4

The main goal of this work is to prove that every entire curve in a smooth hypersurface of degree greater than or equal to 97 in the complex projective space of dimension 4 must satisfy an algebraic differential equation of order 3. A logarithmic version of this result is given proving that every entire curve in the complement of a smooth surface of degree greater than or equal to 92 in the complex projective space of dimension 3 must satisfy an algebraic differential equation of order 3.

math.AG↗
arXiv2006

On the logarithmic Kobayashi conjecture

We study the hyperbolicity of the log variety $(\mathbb{P}^n, X)$, where $X$ is a very general hypersurface of degree $d\geq 2n+1$ (which is the bound predicted by the Kobayashi conjecture). Using a positivity result for the sheaf of (twisted) logarithmic vector fields, which may be of independent interest, we show that any log-subvariety of $(\mathbb{P}^n, X)$ is of log-general type, give a new proof of the algebraic hyperbolicity of $(\mathbb{P}^n, X)$, and exclude the existence of maximal rank families of entire curves in the complement of the universal degree $d$ hypersurface. Moreover, we prove that, as in the compact case, the algebraic hyperbolicity of a log-variety is a necessary condition for the metric one.

math.AG↗