Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces
| dc.creator | Zuo, Kang | |
| dc.creator | Viehweg, Eckart | |
| dc.date | 2003-07-31 | |
| dc.date | 2003-09-30 | |
| dc.date.accessioned | 2026-07-07T04:59:59Z | |
| dc.date.available | 2026-07-07T04:59:59Z | |
| dc.description | Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space, ramified over a hypersurface of degree d. Iterating this construction, one obtains M(d,n;r). We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa coupling degenerates for d<2n. On the other hand, for all d>n the sub-stack M(d,n;2) deforms. We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r), and we construct a 4-dimensional family of quintic hypersurfaces, and a dense set of points in the base, where the fibres have complex multiplication. | |
| dc.description | 38 pages, amsLaTeX, second version: Correction of a wrong statment in Section 8; References updated, some typos corrected (including one in the title) | |
| dc.identifier | https://arxiv.org/abs/math/0307398 | |
| dc.identifier | http://arxiv.org/abs/math/0307398 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68213 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14J70; 14D05; 14D07; 14J32 | |
| dc.title | Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces | |
| dc.type | text |