6533b870fe1ef96bd12cf3e3
RESEARCH PRODUCT
Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces
Eckart ViehwegKang Zuosubject
Algebra and Number TheoryDegree (graph theory)Mathematics - Complex Variables14D0514J3214D07Complex multiplicationYukawa potentialRigidity (psychology)14J70ModuliCombinatoricsAlgebraMathematics - Algebraic Geometry14J70; 14D05; 14D07; 14J32HypersurfaceMathematics::Algebraic GeometryMathematikFOS: MathematicsGeometry and TopologyComplex Variables (math.CV)Algebraic Geometry (math.AG)Stack (mathematics)Mathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-07-31 |