Normality of minimal log canonical centers of threefolds in mixed and positive characteristic

We prove the normality of minimal log canonical centers on threefold pairs whose residue fields are perfect of residue characteristics <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>≠</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>5</mml:mn> </mml:math> . We also show that the union of all log canonical centers on threefold pairs with standard coefficients are seminormal provided that the residue characteristics are large enough. In contrast, we provide an example of a non-seminormal log canonical center on a threefold in characteristic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> </mml:math> , and give sufficient conditions to construct similar examples.