AI 中文总结
本文给出LVMB流形代数维数的精确上界，并与下界比较得到精确值，同时描述其代数约化，用环面拟流形的非理性度计算双亚纯不变量。
AI 中文摘要
LVMB流形是由代数-组合数据构造的一大类紧致复非Kähler且非代数流形。我们给出了其代数维数的上界，并证明了该上界是精确的。将我们的结果与Meersseman发现的下界进行比较，在许多相关情形下，我们获得了LVMB流形的精确代数维数。进一步分析后，我们还得到了LVMB流形代数约化的描述。由此可知，Meersseman的下界与有理分量的维数一致。这一LVMB流形的双亚纯不变量随后用相伴的环面拟流形的非理性度来计算。该不变量是Battaglia和Prato最近引入的，我们为其提供了显式公式。
英文摘要
LVMB manifolds are a large class of compact complex non-Kähler and non-algebraic manifolds, constructed from an algebro-combinatorial datum. We provide an upper bound on their algebraic dimension and prove it to be sharp. Comparing our result with the lower bound found by Meersseman, we obtain the exact algebraic dimension of an LVMB manifold in many relevant cases. Pursuing our analysis further, we also obtain a description of the algebraic reduction of an LVMB manifold. From this, it emerges that Meersseman's lower bound coincides with the dimension of the rational component. This bimeromorphic invariant of an LVMB manifold is then computed in terms of the nonrationality degree of the associated toric quasifold. This is an invariant recently introduced by Battaglia and Prato, for which we provide an explicit formula.
