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- W3196344689 abstract "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." @default.
- W3196344689 created "2021-09-13" @default.
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- W3196344689 date "2021-08-31" @default.
- W3196344689 modified "2023-09-23" @default.
- W3196344689 title "Torus actions, Morse homology, and the Hilbert scheme of points on affine space" @default.
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- W3196344689 doi "https://doi.org/10.46298/epiga.2021.6792" @default.
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