论文标题
在准平滑的calabi-yau hypersurfaces的镜子的巨大霍奇数字上
On the stringy Hodge numbers of mirrors of quasi-smooth Calabi-Yau hypersurfaces
论文作者
论文摘要
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 $ d+1 $ lattice vectors $ v_i $满足关系$ \ sum_i w_i v_i = 0 $。在本文中，我们计算了镜子的弦乐$ e $ - $ x^\ vee $，并将其与vafa的orbifold $ e $ - quasi-smooth-smooth calabi-yau hypersurfaces $ x $进行比较。结果，我们证明了霍奇数字的平等性$ h^{p，q} _ {\ rm str}（x^{\ vee}）= h^{d-1-p，q} _ {\ rm orb}（x） 对于所有$ p，q $和$ d $，正如镜像对称性所预期的那样。
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.
