论文标题
局部局部同核复合物表面的扭曲差异和李类
Twisted differentials and Lee classes of locally conformally symplectic complex surfaces
论文作者
论文摘要
我们研究了局部合成符号（LCS）结构的Lee $ 1 $ forms的一组，从而在Kodaira VII类中驯服了紧凑型复杂表面的复杂结构，并表明非平凡/下限的存在与该程度相对于某些负面/非pssh的函数的存在相对于某些范围的函数相对应。我们用它来证明驯服LCS的Lee Derham类集已连接，并在双曲线Kato表面上获得该组的显式负上限。这导致了在已知的VII级复合体表面的已知实例的Lee类的完整描述，以及在中间类型的双曲线KATO表面上存在Bi-Hermitian结构的新障碍。我们的结果还揭示了Lee类集合的边界与非平凡的对数Holomormormormormormormormormormormormormormormormormormormormormormormorphic $ 1 $形式之间的联系，并在平坦的Holomorphic Line Bundle中值。
We study the set of deRham classes of Lee $1$-forms of the locally conformally symplectic (LCS) structures taming the complex structure of a compact complex surface in the Kodaira class VII, and show that the existence of non-trivial upper/lower bounds with respect to the degree function correspond respectively to the existence of certain negative/non-negative PSH functions on the universal cover. We use this to prove that the set of Lee deRham classes of taming LCS is connected, as well as to obtain an explicit negative upper bound for this set on the hyperbolic Kato surfaces. This leads to a complete description of the sets of Lee classes on the known examples of class VII complex surfaces, and to a new obstruction to the existence of bi-hermitian structures on the hyperbolic Kato surfaces of the intermediate type. Our results also reveal a link between bounds of the set of Lee classes and non-trivial logarithmic holomorphic $1$-forms with values in a flat holomorphic line bundle.
