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A note on orderings
on algebraic varieties
Maria Emilia Alonso García |
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Vol. 123 (1986), No. 1, 1–7
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Abstract |
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It was proven in [A-G-R] that if V ⊂ Rn is a surface and α a total ordering in its coordinate polynomial ring, α can be described by a half branch (i.e., there exists γ(0,𝜖) → V , analytic, such that for every f ∈ R[V ]sgnαf = sgnf(γ(t)) for t small enough). Here we prove (in any dimension) that the orderings with maximum rank valuation can be described in this way. Furthermore, if the ordering is centered at a regular point we show that the curve can be extended C∞ to t = 0. |
Mathematical Subject Classification 2000
Primary: 14G30, 14G30
Secondary: 12D15, 12J15
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Milestones
Received: 16 January 1985
Revised: 1 July 1985
Published: 1 May 1986
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Authors |
| Maria Emilia Alonso García | |
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