The Gorenstein conjecture fails for the tautological ring of $\mathcal{\overline{M}}_{2,n}$
The Gorenstein conjecture fails for the tautological ring of $\mathcal{\overline{M}}_{2,n}$
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DOI：
10.1007/s00222-013-0466-z
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发表时间：
2012-10
影响因子：
3.1
通讯作者：
D. Petersen;O. Tommasi
中科院分区：
文献类型：
--
作者：
D. Petersen;O. Tommasi
设为使存在偶次非重言式上同调类的最小整数。我们注意到，在格雷伯和潘达里潘德的作品中，有这样一个非重言式的班级。我们证明了非重言式上同调只有一个度，而不是中度。特别是，它得出的结论是，重言式的环不是戈伦斯坦。我们提出了一些证据，表明N=20成立。
Letbe the smallest integer such that there is a non-tautological cohomology class of even degree on. We remark that there is such a non-tautological class on, by work of Graber and Pandharipande. We show thathas non-tautological cohomology only in one degree, which is not the middle degree. In particular, it follows that the tautological ring ofis not Gorenstein. We present some evidence suggesting that N=20 holds.