episciences.org_6792_1660231303
1660231303
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Épijournal de Géométrie Algébrique
24916765
08
31
2021
Volume 5
Torus actions, Morse homology, and the Hilbert scheme of points on
affine space
Burt
Totaro
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
quasiprojective 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^1homotopy 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 nspace is homotopy equivalent to the subspace consisting
of schemes supported at the origin.
08
31
2021
6792
arXiv:2009.07381
10.48550/arXiv.2009.07381
https://arxiv.org/abs/2009.07381v1
10.46298/epiga.2021.6792
https://epiga.episciences.org/6792

https://epiga.episciences.org/8404/pdf