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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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