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- W2910087775 abstract "We study the Irreducibility Problem for the arc space X∞ of an irreducible singular algebraic variety X defined over a perfect field k of characteristic p>0. The existence of reducible such X∞ is related to the fact that Kolchin's Irreducibility Theorem fails to hold in positive characteristic. We obtain a complete description of the irreducible components of X∞ when X is a surface. Section 5 introduces two main new problems in arbitrary dimension: (1) in the line of O. Zariski and H. Hironaka, blowing up any X to get Y→X with Y∞ irreducible; (2) in the line of J. Nash's work on arcs, characterizing irreducibility in terms of Resolution of Singularities." @default.
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- W2910087775 date "2022-11-01" @default.
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- W2910087775 title "Small irreducible components of arc spaces in positive characteristic" @default.
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- W2910087775 doi "https://doi.org/10.1016/j.jpaa.2022.107110" @default.
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