Search results for "calabi yau"

showing 3 items of 3 documents

Groups acting freely on Calabi-Yau threefolds embedded in a product of del Pezzo surfaces

2011

In this paper, we investigate quotients of Calabi-Yau manifolds $Y$ embedded in Fano varieties $X$, which are products of two del Pezzo surfaces — with respect to groups $G$ that act freely on $Y$. In particular, we revisit some known examples and we obtain some new Calabi-Yau varieties with small Hodge numbers. The groups $G$ are subgroups of the automorphism groups of $X$, which is described in terms of the automorphism group of the two del Pezzo surfaces.

Automorphism groupPure mathematicsGeneral MathematicsGeneral Physics and AstronomyFOS: Physical sciencesFano planeMathematical Physics (math-ph)AutomorphismMathematics - Algebraic GeometryMathematics::Algebraic GeometryProduct (mathematics)FOS: MathematicsCalabi–Yau manifolddel pezzo calabi yauSettore MAT/03 - GeometriaMathematics::Differential GeometryGrupo actions Calabi-Yau threefolds hodge numbersAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryQuotientMathematical PhysicsMathematics
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Quotients of Hypersurfaces in Weighted Projective Space

2009

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 som…

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
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Geometry and arithmetic of Maschke's Calabi-Yau three-fold

2011

Maschke's Calabi-Yau three-fold is the double cover of projective three space branched along Maschke's octic surface. This surface is defined by the lowest degree invariant of a certain finite group acting on a four-dimensional (4D) vector space. Using this group, we show that the middle Betti cohomology group of the three-fold decomposes into the direct sum of 150 2D Hodge substructures. We exhibit 1D families of rational curves on the three-fold and verify that the associated Abel-Jacobi map is non-trivial. By counting the number of points over finite fields, we determine the rank of the Neron-Severi group of Maschke's surface and the Galois representation on the transcendental lattice of…

Pure mathematicsAlgebra and Number TheoryGeneral Physics and AstronomyCalabi–Yau manifoldFold (geology)abel-jacobi map calabi yau varietySettore MAT/03 - GeometriaMathematical PhysicsMathematics
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