Rational simple connectedness and weak approximation
Jason Starr
Stony Brook



Rational simple connectedness is an analogue in algebraic geometry of simple connectedness in topology, just as rational connectedness is an analogue of path connectedness. Given a system of polynomial equations in some (arbitrary) number of variables and depending on one parameter, weak approximation is the problem of approximating power series solutions in the parameter to arbitrary order by polynomial solutions in the parameter. B. Hassett found a simple, elegant connection between rational simple connectedness and weak approximation. Recently A. J. de Jong and I proved all smooth, low degree complete intersections are rationally simply connected, and thus satisfy weak approximation. No background will be assumed.