Mathematics – Algebraic Geometry
Scientific paper
2007-03-05
Int. Math. Res. Pap. 2007 Art. ID rpm005
Mathematics
Algebraic Geometry
41 pages, published version (before page proofs); some typos corrected
Scientific paper
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.
Asok Aravind
Doran Brent
No associations
LandOfFree
On unipotent quotients and some A^1-contractible smooth schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On unipotent quotients and some A^1-contractible smooth schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On unipotent quotients and some A^1-contractible smooth schemes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-235001