Chow rings of moduli spaces of curves II: Some results on the Chow ring of $\overline{\mathscr{M}}_4$
Chow rings of moduli spaces of curves II: Some results on the Chow ring of $\overline{\mathscr{M}}_4$
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曲线模空间 Chow 环 II: $overline{mathscr{M}}_4$ Chow 环的一些结果
DOI：
10.2307/1971526
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发表时间：
1990
影响因子：
4.9
通讯作者：
C. Faber
中科院分区：
文献类型：
--
作者：
C. Faber
亏格为4的稳定曲线的模空间的环。这些结果并不完整。我们发现发电机的周环4和周群的余维1和2的-W 4。对于A2（G '4），我们找到14个生成元。利用测试曲面证明了A2（4/'4）的维数至少为13，并明确地确定了14个生成元之间仍然存在的单一关系.最后，我们有两个证据证明这个关系确实成立，所以A2（4/4）的维数等于13。这使我们能够确定，4 '4的周环。我们最初的证明是基于一个相当微妙的论点;第二个证明使用了冉（见[R]）的结果，并且简单得多。
ring of the moduli space of stable curves of genus 4. These results are not complete. We find generators for the Chow ring of 4 and for the Chow groups in codimension 1 and 2 of -W4. For A2(G'4) we find fourteen generators. Using test surfaces we prove that the dimension of A 2(4/'4) is at least 13 and explicitly determine the single relation between the fourteen generators which still can exist. Finally, we have two proofs that this relation does indeed hold, so that the dimension of A2( 4/4) equals 13. This enables us to determine the Chow ring of ,4'4. Our original proof is based on a rather delicate argument; the second proof uses a result of Ran (see [R]) and is much simpler.