论文标题
对数含量表面和硼酿元素的分析扭转
Analytic torsion for log-Enriques surfaces and Borcherds product
论文作者
论文摘要
我们介绍了索引二的索引表面的全体形态扭转，并带有循环商$ \ frac {1} {1} {4} {4}（1,1）$。 $ k $单数点的此类原木含量表面的模量空间是尺寸$ 10-k $的正交类型的模块化，与签名$（2,10-k）$相关的单型晶格相关。我们证明，不变的彼得森标准是明确的Borcherds产品的彼得森规范。我们注意到，这种扭转本质上是复杂尺寸$ 2 $的BCOV不变性。结果，在这种情况下，BCOV不变并不是与卡拉比Yau案不同的异常不变的。
We introduce a holomorphic torsion invariant of log-Enriques surfaces of index two with cyclic quotient singularities of type $\frac{1}{4}(1,1)$. The moduli space of such log-Enriques surfaces with $k$ singular points is a modular variety of orthogonal type %of dimension $10-k$ associated with a unimodular lattice of signature $(2,10-k)$. We prove that the invariant, viewed as a function on the modular variety, is given by the Petersson norm of an explicit Borcherds product. We note that this torsion invariant is essentially the BCOV invariant in the complex dimension $2$. As a consequence, the BCOV invariant in this case is not a birational invariant, unlike the Calabi-Yau case.
