论文标题
圆环动作，摩尔斯同源性和仿射空间上的希尔伯特方案
Torus actions, Morse homology, and the Hilbert scheme of points on affine space
论文作者
论文摘要
我们在动机同义理论中对乘法群体的作用进行了猜想。简而言之，如果乘积组g_m作用于准标记方案u，以便将u吸引到t接近g_m中的t接近u中的u中u中的闭合子集y，则y到u的包含应该是a^1-homotopy等价。 我们证明了几个部分结果。特别是，在复数上，包含是复杂点上的同质等效性。证明将莫尔斯理论的类似物用于奇异品种。应用：仿射N空间上的Hilbert方案是同等的，等于由原点支持的方案组成的子空间。
We formulate a conjecture on actions of the multiplicative group in motivic homotopy theory. In short, if the multiplicative group G_m acts on a quasi-projective scheme U such that U is attracted as t approaches 0 in G_m to a closed subset Y in U, then the inclusion from Y to U should be an A^1-homotopy equivalence. We prove several partial results. In particular, over the complex numbers, the inclusion is a homotopy equivalence on complex points. The proofs use an analog of Morse theory for singular varieties. Application: the Hilbert scheme of points on affine n-space is homotopy equivalent to the subspace consisting of schemes supported at the origin.
