On algorithmic unsolvability of the problem embeddability of algebraic varieties over a field of characteristic zero

Classification of algebraic varieties is an important problem in the algebraic geometry. The problem of embeddability of two varieties is adjoining. The algorithmic solvability of these problems is a very interesting and fundamental. The problem of embeddability for two varieties over field of zero characteristic is algorithmically unsolvable. This is a recent result by author and A. Ya. Kanel-Belov (2018). In our talk we will prove this and discuss about adjoining problems.