论文标题
关于Batyrev和Bhk镜子对称结构的等效性
On the equivalence of Batyrev and BHK Mirror symmetry constructions
论文作者
论文摘要
我们考虑了Calabi-yau Orbifold的镜子合作伙伴的两个结构之间的联系。此Orbifold被定义为某些合适的亚组$ g $在加权投影空间中的hypersurface $ x_m $的相对的相对符号，由准均匀的多项式$ w_m $切除。首先是Berglund-Hübsch-Krawitz（BHK）结构，它使用了另一个加权的投影空间，并使用了新的Hypersurface $ x_ {m^t} $的商在其中，由某个双重组$ g^t $。在第二个是Batyrev构造中，镜面伴侣被构造为由反身二元组合的倍形品种中的超曲面，与原始的calabi-yau orbifold相关的多层偶。我们给出了简单的证据，证明了这两种结构的等效性。
We consider the connection between two constructions of the mirror partner for the Calabi-Yau orbifold. This orbifold is defined as a quotient by some suitable subgroup $G$ of the phase symmetries of the hypersurface $ X_M $ in the weighted projective space, cut out by a quasi-homogeneous polynomial $W_M$. The first, Berglund-Hübsch-Krawitz (BHK) construction, uses another weighted projective space and the quotient of a new hypersurface $X_{M^T}$ inside it by some dual group $G^T$. In the second, Batyrev construction, the mirror partner is constructed as a hypersurface in the toric variety defined by the reflexive polytope dual to the polytope associated with the original Calabi-Yau orbifold. We give a simple evidence of the equivalence of these two constructions.
