Tue, June 23, 2020
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5:00pm [5:30pm] Mitra Koley, TIFR Mumbai
Description:
Date and Time: 23 June 2020, 5:30 pm IST - 6:30 pm IST (joining time : 5:15 pm IST - 5:30 pm IST) Google Meet Link: https://meet.google.com/gkc-hydx-fkn Speaker: Mitra Koley, TIFR Mumbai Title: $F$-rationality of Rees algebras. Abstract: In this talk we will discuss $F$-rationality of Rees algebras. The study in this direction began when Singh gave an example of $3$-dimensional hypersurface $F$-rational ring whose Rees algebra with respect to a maximal ideal is Cohen-Macaulay and normal domain but not $F$-rational. Motivated by this example Hara, Watanabe and Yoshida investigated various questions regarding $F$-rationality of Rees algebras. Using the notion of tight integral closure they gave a criterion for $F$-rationality of Rees algebras of ideals primary to the maximal ideal of a Cohen-Macaulay local ring. Their paper is of significant interest because of some conjectures and some open questions. In a joint work with Manoj Kummini we study these questions and conjectures and answer some of them.
6:00pm