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Seminar of the Laboratory on Algebraic Transformation Groups HSE University
April 17, 2024 18:00, Moscow, online, for the zoom link contact dchunaev@hse.ru


Rigidity and Rationality of Pham-Brieskorn Threefolds

M. Chitayat

University of Ottawa


https://youtu.be/HPSD0p5VhE4

Abstract: A ring $B$ is said to be rigid if the only locally nilpotent derivation $D: B \rightarrow B$ is the zero derivation. We prove that a $3$-dimensional Pham-Brieskorn ring $B_{a_0, a_1, a_2, a_3} = C[X_0, X_1, X_2, X_3] / ( X_0^{a_0} + X_1^{a_1} + X_2^{a_2} + X_3^{a_3} )$ is not rigid if and only if $a_i = 1$ for some $i$ or $ a_i = a_j = 2$ for distinct $i$ and $j$. We also determine for which $(a_0, a_1, a_2, a_3)$ the ring $B_{a_0, a_1, a_2, a_3} $ is rational. The content in the first part of the talk consists of joint work with Adrien Dubouloz.


© Steklov Math. Inst. of RAS, 2024