Zuo, Kang; Viehweg, Eckart:
Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces
In: Journal of Algebraic Geometry, Vol. 14 (2005), No. 3, pp. 481 - 528
2005article/chapter in journalOpen Access
MathematicsFaculty of Mathematics
Related: 1 publication(s)
Title in English:
Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces
Author:
Zuo, Kang;Viehweg, EckartUDE
LSF ID
5111
Other
connected with university
Year of publication:
2005
Open Access?:
Open Access
Scopus ID
Language of text:
English

Abstract in English:

Let Md,n be the moduli stack of hypersurfaces X ⊂ ℙn of degree d≥ n + 1, and let Md,n (1)be the sub-stack, parameterizing hypersurfaces obtained as a d-fold cyclic covering of ℙn-1 ramified over a hypersurface of degree d. Iterating this construction, one obtains Md,n (ν). We show that Md,n(1) is rigid in M d,n, although for d < 2n the Griffiths-Yukawa coupling degenerates. However, for all d ≥ n + 1 the sub-stack Md,n (2) deforms. We calculate the exact length of the Griffiths-Yukawa coupling over Md,n(ν) and we construct a 4-dimensional family of quintic hypersurfaces g: struck Z sign → T in ℙ4, and a dense set of points t in T, such that g-1(t) has complex multiplication.