On unipotent quotients and some A^1-contractible smooth schemes
| dc.creator | Asok, Aravind | |
| dc.creator | Doran, Brent | |
| dc.date | 2007-03-05 | |
| dc.date | 2007-10-18 | |
| dc.date.accessioned | 2026-07-07T08:36:58Z | |
| dc.date.available | 2026-07-07T08:36:58Z | |
| dc.description | We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together with a cohomological vanishing criterion, to characterize whether or not the resulting quasi-affine quotient scheme is affine. We completely analyze the case of G_a-invariant hypersurfaces in a linear G_a-representation W; here the above characterizations admit simple geometric and algebraic interpretations. As an application, we produce arbitrary dimensional families of non-isomorphic smooth quasi-affine but not affine n-dimensional varieties (n \geq 6) that are contractible in the sense of A^1-homotopy theory. Indeed, existence follows without any computation; yet explicit defining equations for the varieties depend only on knowing some linear G_a- and SL_2- invariants, which, for a sufficiently large class, we provide. Similarly, we produce infinitely many non-isomorphic examples in dimensions 4 and 5. Over C, the analytic spaces underlying these varieties are non-isomorphic, non-Stein, topologically contractible and often diffeomorphic to C^n. | |
| dc.description | 41 pages, published version (before page proofs); some typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0703137 | |
| dc.identifier | http://arxiv.org/abs/math/0703137 | |
| dc.identifier | Int. Math. Res. Pap. 2007 Art. ID rpm005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140245 | |
| dc.subject | Algebraic Geometry | |
| dc.title | On unipotent quotients and some A^1-contractible smooth schemes | |
| dc.type | text |