Description

Commutative algebra Seminar

Thursday, 9 Nov. 4-5 pm

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Venue: Ramanujan Hall

Host: Tony Puthenpurakal

Speaker: R. V. Gurjar, IIT Bombay

Title: Brieskorn-Pham Singularities.

Abstract: Let B=k[X_1,...,X_{n+1}]/(X_1^{a_1}+...+X_{n+1}^{n+1}) where k is the field of complex numbers and X the corresponding affine variety. These have been studied from many angles: (1) Brieskorn-Pham, Milnor, (2) from the topological viewpoint, giving rise to exotic spheres. (3) Storch for calculating the divisor class group of B (4) Flenner, Keichi Watanabe for characterizing rational singularities among them. (4) Recently Michael Chitayat wrote a beautiful thesis at Univ. of Ottawa characterizing 3-dimensional B-P singularities that admit a non-trivial locally nilpotent derivation (which is equivalent to having a G_a action on X). He has solved a conjecture about this completely. (5) I asked Michael which of the 3-dimensional B-P singularities define rational varieties in the sense of function field. Using ideas in his thesis he answered this completely.

Description

Ramanujan Hall, Department of Mathematics

Date

Thu, November 9, 2023

Start Time

4:00pm-5:00pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Sun, November 5, 2023 10:33pm IST