标题： 曼因猜想中巴特列夫和茨金克尔例子的几何例外集 显示英文标题

标题： The geometric exceptional set in Manin's conjecture for Batyrev and Tschinkel's example

摘要： Batyrev和Tschinkel的示例是一个Fermat三次曲面丛$X$，它是一个Fano$5$-流形。 这是第一个对于适当的闭异常集，Manin猜想永远不成立的例子。 最近，Lehmann、Sengupta和 Tanimoto提出了Manin猜想中异常集的一个猜想的几何描述，并证明了它总是包含在一个稀疏集中。 在特征为$0$的域上，我们显式构造有限多个稀疏映射，使得任何具有相等或更大的$a$和 $b$值的稀疏映射$f:Y\rightarrow X$，在字典序下通过其中一个进行有理分解。 特别是，这定义了一个与Lehmann-Sengupta-Tanimoto的猜想异常集一致的稀疏集。 显示英文摘要

摘要： Batyrev and Tschinkel's example is a Fermat cubic surface bundle $X$ which is a Fano $5$-fold. It is the first example for which Manin's conjecture can never hold for a proper closed exceptional set. Recently, Lehmann, Sengupta, and Tanimoto proposed a conjectural geometric description of the exceptional set in Manin's conjecture and showed that it is always contained in a thin set. Over a field of characteristic $0$, we explicitly construct finitely many thin maps such that any thin map $f:Y\rightarrow X$ with equal or larger $a$- and $b$-values in lexicographical order factors rationally through one of them. In particular, this defines a thin set which coincides with Lehmann-Sengupta-Tanimoto's conjectural exceptional set.