Nash modification on toric surfaces

Details Nash modification on toric surfaces Nash modification on toric surfaces

2011-10-19

arxiv.org/abs/1110.4346v1

Mathematics

Algebraic Geometry

20 pages, 9 figures

Scientific paper

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 toric 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 $\nu:\C(x_1,x_2)\rightarrow\Gamma$ is any valuation centered on the toric surface and such that $\nu(x_1)\neq\lambda\nu(x_2)$ for all $\lambda\in\R\setminus\Q$, then a finite iteration of Nash modification gives local uniformization along $\nu$.

Affiliated with

Also associated with

No associations

Rating

Nash modification on toric surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nash modification on toric surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nash modification on toric surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-597741