Commutative algebra Seminar
Thursday, 09/03/2023, 4 pm
Venue: Ramanujan Hall
Host: Tony J. Puthenpurakal
Speaker: Prof. R. V. Gurjar
Affiliation: Former Professor, IIT Bombay
Title: Positively Graded domain
Abstract: I will continue my lectures on this topic. Following results will be discussed. 1. Demazure's construction of normal affine positively graded domains. Some applications of this will be discussed. 2. Flenner and Keiichi Watanabe's rationality of singularities criterion for positively graded affine domains. 3. A very general result I conjectures around 1990 and proved by O.Mathieu In 2002 will be discussed. It has some new consequence for rings of invariants of reductive algebraic group action on an affine space. 4. Divisor Class Groups of positively draded domains. Works of Brieskon Flenner, Samuel, Scheja-Storch, Anurag Singh etc, will be mentioned. Connection with Topology of these results will be discussed.