6533b862fe1ef96bd12c6e7d

RESEARCH PRODUCT

Deformations of Calabi-Yau manifolds in Fano toric varieties

Gilberto BiniDonatella Iacono

subject

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

description

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.

yearjournalcountryeditionlanguage
2020-05-12
https://dx.doi.org/10.48550/arxiv.2005.05582