Year: 1995
Type: article
Abstract: Let Xd C ]p'n+i be a smooth hypersurface.If d ~ n + 2 then Xd contains very few rational curves.If d:::; n + 1 then Xd is covered by rational curves, in fact any two points can be connected by a rational curve in X d • The best known algebraic variety with lots of rational curves is ]p'n, and early on the question was raised if these hypersurfaces are birational to ]p'n or not.It is easy to see that Xd is rational if d = 2 (project Xd from any of its points).It is less clear, but has been know for a hundred years, that any smooth cubic in ]p'3 is rational.
Author: János Kollár
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W4246367739