BibTeX
@MISC{n.n.08tameideals,
author = {n.n.},
title = {TAME IDEALS AND BLOWUPS},
year = {2008}
}
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Abstract
We study blowups of affine n-space An K = Spec(K[x1,..., xn]) with center an arbitrary monomial ideal I. We give a combinatorial criterion to decide wether eA n K is smooth. It just uses the Newtonpolyhedron associated to the monomial ideal. We call monomial ideals which produce a smooth blowup e An K tame ideals. In case of a singular blowup we describe a smoothening procedure proposed by Rosenberg [20]. Further we study blowups in products of coordinate ideals. In particular we examine the question when such a product is tame. In this context we turn our attention to monomial building sets. Building Sets were introduced by DeConcini and Procesi [1] in order to construct wonderful models of linear subspace arrangements. We prove that a product of coordinate ideals, which form a building set, is tame. We also show that this condition is not necessary, i.e., that there exist tame products of coordinate ideals, which do not form a building set.
