6533b7d2fe1ef96bd125ebc4
RESEARCH PRODUCT
A closer look at mirrors and quotients of Calabi-Yau threefolds
Gilberto BiniFilippo F. Favalesubject
Pure mathematics010308 nuclear & particles physics010102 general mathematicsToric varietyPolytopeFano varietymirror symmetry01 natural sciencesTheoretical Computer ScienceMathematics::Algebraic GeometryMathematics (miscellaneous)0103 physical sciencesCalabi-YauCrepant resolutionCalabi–Yau manifoldMirror Symmetry Calabi-Yau QuotientsSettore MAT/03 - Geometria0101 mathematicsMathematics::Symplectic GeometryQuotientOrbifoldMAT/03 - GEOMETRIAMathematicsResolution (algebra)description
Let X be the toric variety (P1)4 associated with its four-dimensional polytope 1. Denote by X˜ the resolution of the singular Fano variety Xo associated with the dual polytope 1o. Generically, anticanonical sections Y of X and anticanonical sections Y˜ of X˜ are mirror partners in the sense of Batyrev. Our main result is the following: the Hodge-theoretic mirror of the quotient Z associated to a maximal admissible pair (Y, G) in X is not a quotient Z˜ associated to an admissible pair in X˜ . Nevertheless, it is possible to construct a mirror orbifold for Z by means of a quotient of a suitable Y˜. Its crepant resolution is a Calabi-Yau threefold with Hodge numbers (8, 4). Instead, if we start from a non-maximal admissible pair, in the same case, its mirror is the quotient associated to an admissible pair.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-02-25 |