Uniform Approximation of Abhyankar Valuation Ideals in Smooth Function Fields
نویسنده
چکیده
Let R be an n-dimensional regular local domain essentially of finite type over a ground field k of characteristic zero, and let ν be a rank one valuation centered on R. Recall that this is equivalent to asking that ν be an R-valued valuation on the fraction field K of R, taking non-negative values on R and positive values on the maximal ideal m ⊆ R. A theorem of Zariski and Abhyankar states that trans.deg ν + rat.rank ν ≤ dimK/k, (1)
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