On the zero locus of ideals defining the Nash blowup of toric surfaces

ABSTRACT

We consider the problem of finding an ideal whose blowup defines the Nash blowup of a toric surface and such that its zero locus coincides with the singular set of the toric surface.

KEYWORDS:

• Nash blowup
• singular locus
• toric surfaces

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 14M25, 14J17
• Secondary: 14E15

Acknowledgements

The second author would like to thank Arturo Giles for the discussions on his results in [8]. Those discussions motivated the question that we explored in this paper. We want to thank the referee for his/her careful reading and helpful comments that improved the presentation of this paper and also for the reference [14].