论文标题
关于希尔伯特计划的理性共同学的生成者的关系
On Generators and Relations of the Rational Cohomology of Hilbert Schemes
论文作者
论文摘要
我们考虑为$ d \ geq 1 $分级的交换$ \ mathbb {q} $ - 代数$ \ mathcal {a}（d）（d）：= h^*（\ operatorAtorName {hilb}^d（\ shilb}^d（\ mathbb {c}^2）第一作者。这些Hurwitz空间反过来又与带边界的Riemann表面的模量空间有关。我们确定了$ \ lfloor d/2 \ rfloor $ $ \ Mathcal {a}（d）$的两个不同的最小值。此外，我们证明何时发生最低程度的生成关系。对于$ d $的少量值，我们还确定了一组最小的生成关系集，这导致了一些关于$ \ Mathcal {a}（d）$的必要生成关系的猜想。
We consider for $d\geq 1$ the graded commutative $\mathbb{Q}$-algebra $\mathcal{A}(d):=H^*(\operatorname{Hilb}^d(\mathbb{C}^2);\mathbb{Q})$, which is also connected to the study of generalised Hurwitz spaces by work of the first author. These Hurwitz spaces are in turn related to the moduli spaces of Riemann surfaces with boundary. We determine two distinct, minimal sets of $\lfloor d/2\rfloor$ multiplicative generators of $\mathcal{A}(d)$. Additionally, we prove when the lowest degree generating relations occur. For small values of $d$ we also determine a minimal set of generating relations, which leads to several conjectures about the necessary generating relations for $\mathcal{A}(d)$.
