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On compactifications of the Steinberg zero-fiber

Thomas Haahr Lynderup·Jesper Funch Thomsen
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Abstract

Let G be a connected semisimple linear algebraic group over an algebraically closed field k of positive characteristic and let X denote an equivariant embedding of G. We define a distinguished Steinberg fiber N in G, called the zero-fiber, and prove that the closure of N within X is normal and Cohen-Macaulay. Furthermore, when X is smooth we prove that the closure of N is a local complete intersection.

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Thomas Haahr Lynderup, Jesper Funch Thomsen. 2005-06-17. On compactifications of the Steinberg zero-fiber. https://arxiv.org/abs/math/0506348

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