Search results for "14J70"

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Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces

2003

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 ha…

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)Mathematics
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Skeleta of affine hypersurfaces

2014

A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.

Pure mathematicsPolynomialMathematicsofComputing_GENERALAffinePolytopeComplex dimensionTopological spaceTriangulation14J70Mathematics - Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsHomotopy equivalenceAlgebraic Topology (math.AT)Mathematics - Algebraic TopologyKato–Nakayama spaceAlgebraic Geometry (math.AG)SkeletonMathematicsToric degenerationTriangulation (topology)HomotopyLog geometry14J70 14R99 55P10 14M25 14T05RetractionHypersurfaceHypersurfaceNewton polytopeSettore MAT/03 - GeometriaGeometry and TopologyAffine transformationKato-Nakayama space14R99
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