Effective algebraic degeneracy

By Simone Diverio, Joël Merker, Erwan Rousseau. 2008

91 citations recorded by the source corpus.

AbstractWe show that for every smooth projective hypersurface X⊂ℙn+1 of degree d and of arbitrary dimension n≥2, if X is generic, then there exists a proper algebraic subvariety Y⊊X such that every nonconstant entire holomorphic curve f:ℂ→X has image f(ℂ) which lies in Y, as soon as its degree satisfies the effective lower bound $d\geqslant 2^{n^{5}}$ .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9555dd8c1ada8fd164b5f5e0490ccc9072da0209

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In Applied Mathematics

1. Damian Brotbek
2. Y. Siu
3. Joël Merker
4. J. Demailly
5. Mihai Paun
6. Qi’an Guan
7. Xiangyu Zhou
8. Junyan Cao

In Geometry and Topology

1. Damian Brotbek
2. Y. Siu
3. Joël Merker
4. J. Demailly
5. Qi’an Guan
6. Mihai Paun
7. Xiangyu Zhou
8. Junyan Cao

Citations in the corpus

• On the hyperbolicity of general hypersurfaces (2016, methodology): “Building on [24], Diverio and Trapani [26] proved that the Kobayashi conjecture holds for (very) general hypersurfaces in P(4) of degree d > 593.”
• Hyperbolicity of generic high-degree hypersurfaces in complex projective space (2012, methodology): “Recently Diverio, Merker, and Rousseau in [8] used the theorem of Riemann–Roch to construct a holomorphic jet differential on X (α) vanishing on an ample divisor and then used Merker’s work [16] involving our method”
• Low pole order frames on vertical jets of the universal hypersurface (2008, methodology): “Indeed, 4 As a result, our two theorems can be applied in the framework o f Demailly-Semple jets ([6]).”