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An Algebraic characterization of the affine three space in arbitrary characteristic (2308.05424v4)

Published 10 Aug 2023 in math.AC and math.AG

Abstract: We give an algebraic characterization of the affine $3$-space over an algebraically closed field of arbitrary characteristic. We use this characterization to reformulate the following question. Let $$A=k[X, Y, Z, T]/(XY+Z{pe}+T+T{sp})$$ where $pe\nmid sp$, $sp\nmid pe$, $e, s\geq 1$ and $k$ is an algebraically closed field of positive characteristic $p$. Is $A= k{[3]}$? We prove some results on ML and ML$*$ invariants and use them to prove a special case of the strong cancellation of $k{[2]}$.

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