Commutative Algebra Seminar

Thursday,  16 February, 4 pm

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Venue: Ramanujan  Hall

Host: Tony Puthenpurakal

Speaker: Prof. R. V. Gurjar

Affiliation: IIT Bombay

Title: Positively Graded Domains

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 conjectured around 1990 and proved by O.Mathieu In 2002 will be discussed. It has some new consequences for rings of invariants of reductive algebraic group action on an affine space.  4. Divisor Class Groups of positively graded domains. Works of Brieskon Flenner, Samuel, Scheja-Storch, Anurag Singh etc, will be mentioned. The connection with the topology of these results will be discussed.