论文标题
通过差异层的$λ$ - 类计算
Computation of $λ$-classes via strata of differentials
论文作者
论文摘要
我们介绍了一个新的重言式关系家族，该家族的模量空间是$ g $的稳定曲线。这些关系是通过计算霍奇束中的空心基因座的庞加莱对二类类获得的。我们使用这些关系来获得霍奇束的Chern类的新表达式。我们证明，$（g-i）$ th类可以表示为重言式班级的线性组合，仅涉及稳定图，最多涉及$ i $ loops。尤其是顶级切恩类可以用树木表达。这一属性是由于Buryak-Guéré-Rossi的DR/DZ等价猜想所致。
We introduce a new family of tautological relations of the moduli space of stable curves of genus $g$. These relations are obtained by computing the Poincaré-dual class of empty loci in the Hodge bundle. We use these relations to obtain a new expression for the Chern classes of the Hodge bundle. We prove that the $(g-i)$th class can be expressed as a linear combination of tautological classes involving only stable graphs with at most $i$ loops. In particular the top Chern class may be expressed with trees. This property was expected as a consequence of the DR/DZ equivalence conjecture by Buryak-Guéré-Rossi.
