论文标题
关于$ \ mathit {sym}^n（¶^1）$的某些子空间的共同体和Occam的Hodge结构的剃须刀
On the cohomology of certain subspaces of $\mathit{Sym}^n(¶^1)$ and Occam's razor for Hodge structures
论文作者
论文摘要
在\ cite {vakil13} vakil和木材中，基于动机Zeta函数的计算，对几何不可还原品种的对称能力做出了几种猜想。这些猜想中的两个大约是$ \ sym^n（¶^1）$的子空间。在本说明中，我们反驳了其中一个，从而获得了Occcam剃须刀原理的霍奇结构原理的反例。我们证明，另一项猜想的措施较小，是正确的。
In \cite{Vakil13} Vakil and Wood made several conjectures on the topology of symmetric powers of geometrically irreducible varieties based on their computations on motivic zeta functions. Two of those conjectures are about subspaces of $\Sym^n(¶^1)$. In this note, we disprove one of them thereby obtaining a counterexample to the principle of Occcam's razor for Hodge structures; and we prove that the other conjecture, with a minor correction, holds true.
