Quotients of Hypersurfaces in Weighted Projective Space

2009/05/13 by Gilberto Bini, Bini, Gilberto
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.0905.2099

arxiv created 2009/05/13 · arxiv updated 2009/12/01

Abstract

In [1] 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 X_A and M_A in weighted projective space and in \mathbb Pⁿ, respectively. The variety M_A turns out to be a quotient of a Fermat variety by a finite group. As a by-product, X_A is a quotient of a Fermat variety and M_A is a quotient of X_A by a finite group. We apply this construction to some families of Calabi-Yau manifolds in order to show their birationality.

Related

• Birational geometry of hypersurfaces in products of weighted projective spaces
• Mirror Quintics, discrete symmetries and Shioda Maps
• The Number of Rational Quartics on Calabi-Yau hypersurfaces in Weighted Projective Space P(2,1⁴)
• Calabi-Yau threefolds in weighted flag varieties
• Motives and mirror symmetry for Calabi-Yau orbifolds