Realization of a certain class of semi-groups as value semi-groups of valuations

Details Realization of a certain class of semi-groups as value semi-groups of valuations Realization of a certain class of semi-groups as value semi-groups of valuations

2008-05-27

arxiv.org/abs/0805.4056v1

Mathematics

Algebraic Geometry

To be Published in BIMS

Scientific paper

Given a well-ordered semi-group $\Gamma$ with a minimal system of generators of ordinal type at most $\omega n$ and of rational rank $r$, which satisfies a positivity and increasing condition, we construct a zero-dimensional valuation centered on the ring of polynomials with $r$ variables such that the semi-group of the values of the polynomial ring is equal to $\Gamma$. The construction uses a generalization of Favre and Jonsson's version of MacLane's sequence of key-polynomials.

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