Non-finitely generated polynomial subalgebras and polynomial automorphism
Speaker: Shigeru Kuroda (Hokkaido University, Japan)

Time: 9h00,Wednesday, May 2, 2018
Location: Room semina 6 Flor, Building A6, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Hilbert's fourteenth problem asks whether certain kind of subalgebras of a polynomial ring are finitely generated. The first counterexample to this problem was given by Nagata in 1958. In this talk, we present a technique for "converting" a given subalgebra (with some mild conditions) into a non-finitely generated subalgebra using a polynomial automorphism. As a consequence, we obtain a number of counterexamples to Hilbert's fourteenth problem and its generalization by Zariski.