Low pole order frames on vertical jets of the universal hypersurface
| dc.creator | Merker, Joel | |
| dc.date | 2008-05-26 | |
| dc.date | 2008-12-16 | |
| dc.date.accessioned | 2026-07-07T12:12:35Z | |
| dc.date.available | 2026-07-07T12:12:35Z | |
| dc.description | Of the two techniques introduced by Bloch, Green-Griffiths and developed by Siu, Demailly to establish Kobayashi hyperbolicity of generic high degree complex algebraic hypersurfaces X in P^(n+1), the second one, initiated by Clemens, Ein, Voisin and developed by Siu, Paun, Rousseau consists in constructing meromorphic frames on the space of the so-called vertical k-jets J_vert^k (X_univ) of the universal hypersurface X_univ parametrizing all X in P^(n+1) of degree d. In 2004, Siu announced that there exists a constant c_n such that the twisting of the tangent bundle to J_vert^n (X_univ) by O (c_n) is globally generated (frame property). The present article provides c_n = (n^2 + 5n) / 2, recovering c_2 = 7 (Paun), c_3 = 12 (Rousseau). Applications to effective degree estimates for algebraic degeneracy or hyperbolicity are expected, especially in dimension n = 4, granted that the Demailly-Semple algebra of jet polynomials invariant under reparametrization and under a certain unipotent action is, for n = k = 4, generated by 16 fundamental bi-invariants enjoying 41 groebnerized syzygies. | |
| dc.description | Major improvement yielding strong (instead of weak) Green-Griffiths algebraic degeneracy in 0811.2346 | |
| dc.identifier | https://arxiv.org/abs/0805.3987 | |
| dc.identifier | http://arxiv.org/abs/0805.3987 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210592 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32Q45; 14N05, 14J70 | |
| dc.title | Low pole order frames on vertical jets of the universal hypersurface | |
| dc.type | text |