6533b859fe1ef96bd12b6fd7

RESEARCH PRODUCT

Quotients of Hypersurfaces in Weighted Projective Space

Gilberto Bini

subject

Fermat's Last TheoremFinite groupPure mathematicscalabi yau weighted projective spacelaw.inventionMathematics - Algebraic GeometryInvertible matrixMathematics::Algebraic GeometryIntegerlawFOS: MathematicsOrder (group theory)Geometry and TopologySettore MAT/03 - GeometriaVariety (universal algebra)Weighted projective spaceAlgebraic Geometry (math.AG)QuotientMathematics

description

Abstract In [Bini, van Geemen, Kelly, Mirror quintics, discrete symmetries and Shioda maps, 2009] some quotients of one-parameter families of Calabi–Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More specifically, let A be an invertible matrix with non-negative integer entries. We introduce varieties XA and in weighted projective space and in , respectively. The variety turns out to be a quotient of a Fermat variety by a finite group. As a by-product, XA is a quotient of a Fermat variety and is a quotient of XA by a finite group. We apply this construction to some families of Calabi–Yau manifolds in order to show their birationality.

yearjournalcountryeditionlanguage
2009-05-13
10.1515/advgeom.2011.029http://hdl.handle.net/10447/398162