Nash modification on toric surfaces

作者：Duarte Daniel^*

来源：Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas, 2014, 108(1): 153-171.

DOI：10.1007/s13398-012-0104-4

• Toric surface
• Nash modification
• Combinatorial algorithm

It has been recently shown that the iteration of Nash modification on not necessarily normal toric varieties corresponds to a purely combinatorial algorithm on the generators of the semigroup associated to the toric variety. We will show that for tone surfaces this algorithm stops for certain choices of affine charts of the Nash modification. In addition, we give a bound on the number of steps required for the algorithm to stop in the cases we consider. Let C(x(1),x(2)) be the field of rational functions of a toric surface. Then our result implies that if nu : C(x(1),x(2)) -%26gt; Gamma is any valuation centered on the toric surface and such that nu (x(1)) not equal lambda nu (x(2)) for all lambda epsilon R \ Q, then a finite iteration of Nash modification gives local uniformization along nu.

• 出版日期2014