|
Acyclic varieties are by definition complex varieties with integral or
rational singular homologies isomorphic to that of a point. Contractible
varieties are important examples of acyclics. I will introduce acyclic
curves, surfaces and threefolds with the aim of demonstrating their rich
structure and their relation to questions of rationality and Zariski's
cancellation problem. I will also report on a joint work with Gurjar about
C*-fibrations on special type affine surfaces which are complete
intersections and its consequences for acyclic surfaces.
|