6533b853fe1ef96bd12ac2c8
RESEARCH PRODUCT
Mirror quintics, discrete symmetries and Shioda maps
Tyler L. KellyBert Van GeemenGilberto Binisubject
High Energy Physics - TheoryPure mathematicsAlgebra and Number TheoryHolomorphic functionFOS: Physical sciencesSymmetry groupPicard–Fuchs equationQuintic functionAlgebraMathematics - Algebraic GeometryMathematics::Algebraic GeometryHigh Energy Physics - Theory (hep-th)mirror symmetry shioda mapsHomogeneous spaceFOS: MathematicsProjective spaceCalabi–Yau manifoldSettore MAT/03 - GeometriaGeometry and TopologyAlgebraic Geometry (math.AG)QuotientMathematicsdescription
In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard Fuchs equation associated to the holomorphic 3-form. In this paper we give an easy argument, involving the family of Mirror Quintics, which implies this result. Using a construction due to Shioda, we also relate certain quotients of these one parameter families to the family of Mirror Quintics. Our constructions generalize to degree n Calabi Yau varieties in (n-1)-dimensional projective space.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-09-10 | Journal of Algebraic Geometry |