In [1] some quotients of one-parameter families of Calabi-Yau va- rieties 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 MA in weighted projective space and in Pn, respectively. The variety MA 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 MA 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.

G. Bini (2011). Quotients of Hypersurfaces in Weighted Projective Space. ADVANCES IN GEOMETRY, 11(4), 653-667 [10.1515/ADVGEOM.2011.029].

Quotients of Hypersurfaces in Weighted Projective Space

G. Bini
2011-01-01

Abstract

In [1] some quotients of one-parameter families of Calabi-Yau va- rieties 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 MA in weighted projective space and in Pn, respectively. The variety MA 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 MA 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.
Settore MAT/03 - Geometria
G. Bini (2011). Quotients of Hypersurfaces in Weighted Projective Space. ADVANCES IN GEOMETRY, 11(4), 653-667 [10.1515/ADVGEOM.2011.029].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/398162
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