0000000000847346

AUTHOR

Donatella Iacono

0000-0003-2739-5746

showing 2 related works from this author

Diffeomorphism classes of Calabi-Yau varieties

2016

In this article we investigate diffeomorphism classes of Calabi-Yau threefolds. In particular, we focus on those embedded in toric Fano manifolds. Along the way, we give various examples and conclude with a curious remark regarding mirror symmetry.

Mathematics - Differential Geometry14J32 14J45Mathematics - Algebraic GeometryMathematics::Algebraic GeometryDifferential Geometry (math.DG)FOS: MathematicsSettore MAT/03 - GeometriaMathematics::Differential GeometryAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryCalabi-Yau diffeomorphism
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Deformations of Calabi-Yau manifolds in Fano toric varieties

2020

In this article, we investigate deformations of a Calabi-Yau manifold $Z$ in a toric variety $F$, possibly not smooth. In particular, we prove that the forgetful morphism from the Hilbert functor $H^F_Z$ of infinitesimal deformations of $Z$ in $F$ to the functor of infinitesimal deformations of $Z$ is smooth. This implies the smoothness of $H^F_Z $ at the corresponding point in the Hilbert scheme. Moreover, we give some examples and include some computations on the Hodge numbers of Calabi-Yau manifolds in Fano toric varieties.

Pure mathematicsGeneral MathematicsInfinitesimalFano plane01 natural sciencesMathematics - Algebraic GeometryMorphismMathematics::Algebraic GeometryMathematics::Category TheoryFOS: MathematicsCalabi–Yau manifold0101 mathematicsMathematics::Symplectic GeometryAlgebraic Geometry (math.AG)ComputingMethodologies_COMPUTERGRAPHICSMathematicsFunctorComputer Science::Information Retrieval010102 general mathematicsToric varietyFano toric varieties · Calabi-Yau manifolds · Deformations of subvarietiesManifold010101 applied mathematicsHilbert scheme14J32 14J45 32G10Settore MAT/03 - GeometriaMathematics::Differential Geometry
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