论文标题
11属的生物基因座
The bielliptic locus in genus 11
论文作者
论文摘要
$ \ MATHCAL {M} _g $的Chow环是由$ g \ leq 9 $生成的。同时，由于van Zelm，在$ \ Mathcal {M} _ {G} $上的非tautlogical类的第一个示例是$ \ Mathcal {M} _ {12} $中的Bielliptic基因座的基本类。如果$ \ Mathcal {M} _ {10} $和$ \ Mathcal {M} _ {11} $的杂烩环由耕术类别生成。在这些情况下，自然要看的是在生物座位上。在$ 10 $的属中，众所周知，在生物志上支持的课程是重言式学的。在这里，我们证明了Bielliptic基因座支撑的所有班级都是重言式的，属于$ 11 $。通过Looijenga的消失定理，这意味着它们都消失了。
The Chow ring of $\mathcal{M}_g$ is known to be generated by tautological classes for $g \leq 9$. Meanwhile, the first example of a non-tautological class on $\mathcal{M}_{g}$ is the fundamental class of the bielliptic locus in $\mathcal{M}_{12}$, due to van Zelm. It remains open if the Chow rings of $\mathcal{M}_{10}$ and $\mathcal{M}_{11}$ are generated by tautological classes. In these cases, a natural first place to look is at the bielliptic locus. In genus $10$, it is already known that classes supported on the bielliptic locus are tautological. Here, we prove that all classes supported on the bielliptic locus are tautological in genus $11$. By Looijenga's vanishing theorem, this implies that they all vanish.
