论文标题
小尺寸或大皮卡德数字的复曲面fano歧管的刚性刚度
Cohomological rigidity for toric Fano manifolds of small dimensions or large Picard numbers
论文作者
论文摘要
复曲面歧管的刚性刚度问题询问是否有同构的共同体学是同构的。已经获得了许多肯定的部分解决方案，并且没有反例。在本文中，我们研究了带有$ d = 3,4 $或PICARD NUMBER $ \ GE 2D-2 $的Etric Fano $ d $ folds的差异分类。特别是，我们表明，除两个感谢您的fano $ 4 $折叠外，如果它们的积分共同体学是同构的，则这些歧管是差异的。异常的两个福特fano $ 4 $ folds（Øbro列表中的ID数字为50和57）具有同构的共同体学环，其总庞特拉金类别在同构圈之间保存下来，但我们不知道它们是否是差异性或同源性的。
The cohomological rigidity problem for toric manifolds asks whether toric manifolds are diffeomorphic (or homeomorphic) if their integral cohomology rings are isomorphic. Many affirmative partial solutions to the problem have been obtained and no counterexample is known. In this paper, we study the diffeomorphism classification of toric Fano $d$-folds with $d=3,4$ or with Picard number $\ge 2d-2$. In particular, we show that those manifolds except for two toric Fano $4$-folds are diffeomorphic if their integral cohomology rings are isomorphic. The exceptional two toric Fano $4$-folds (their ID numbers are 50 and 57 on a list of Øbro) have isomorphic cohomology rings and their total Pontryagin classes are preserved under an isomorphism between their cohomology rings, but we do not know whether they are diffeomorphic or homeomorphic.
