Additive group actions: quotients, invariants, and cancellation (Q2479932)

The paper contains a very clearly written survey of recent results on actions of the additive group of complex numbers on affine and quasiaffine varieties. The main personages are proper actions, geometric quotients, free actions, local and global trivializations, the algebra of invariants, locally nilpotent derivations. A special attention is paid to actions on surfaces and threefolds. The section devoted to dimension four contains interesting conjectures and partial positive results. In the last section, the author discusses the generalized cancellation problem, Danielewski's surfaces and Makar-Limanov's invariant.