I algebraic geometry

Relation to the state-of-the-art:

Affine algebraic geometry was initiated by Abhyankar and Nagata in late 1970 and 1980' and then developed by many researchers both in Europe and US. In the Objectives a), d) and e) the team obtained important results.

In some aspects, e.g. for study of bifurcation points or Abhyankar-Moh Problem, results of Jelonek with co-authors [1, 3, 5, 7, 9] provide the best current results.

Objective f) has been little studied in the literature. The paper (24) of Jelonek and Janeczko seems to be the beginning of the story. Objective e) is based on an interesting observation of Jelonek [12] and is a good direction to solve Zariski Cancellation Problem in general.