On the stringy Hodge numbers of mirrors of quasi-smooth Calabi-Yau hypersurfaces Article Swipe

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Victor V. Batyrev ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2006.15825

Mirrors $X^{\vee}$ of quasi-smooth Calabi-Yau hypersurfaces $X$ in weighted projective spaces ${\Bbb P}(w_0, \ldots, w_d)$ can be obtained as Calabi-Yau compactifications of non-degenerate affine toric hypersurfaces defined by Laurent polynomials whose Newton polytope is the lattice simplex spanned by $d+1$ lattice vectors $v_i$ satisfying the relation $\sum_i w_i v_i =0$. In this paper, we compute the stringy $E$-function of mirrors $X^\vee$ and compare it with the Vafa's orbifold $E$-function of quasi-smooth Calabi-Yau hypersurfaces $X$. As a result, we prove the equalities of Hodge numbers $h^{p,q}_{\rm str}(X^{\vee}) = h^{d-1-p,q}_{\rm orb}(X)$ for all $p, q$ and $d$ as it is expected in mirror symmetry.

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Calabi–Yau manifold Orbifold Polytope Degenerate energy levels Mathematics Mirror symmetry Pure mathematics Lattice (music) Affine transformation Physics Combinatorics Quantum mechanics Acoustics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2006.15825
PDF: https://arxiv.org/pdf/2006.15825
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Cited By: 2
References: 22
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DOI: https://doi.org/10.48550/arxiv.2006.15825

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Title: On the stringy Hodge numbers of mirrors of quasi-smooth Calabi-Yau hypersurfaces

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Publication year: 2020

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Publication date: 2020-06-29

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Authors: Victor V. Batyrev

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Concepts: Calabi–Yau manifold, Orbifold, Polytope, Degenerate energy levels, Mathematics, Mirror symmetry, Pure mathematics, Lattice (music), Affine transformation, Physics, Combinatorics, Quantum mechanics, Acoustics

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