Type: Article

Nash modification on toric surfaces

Duarte, Daniel;

Abstract:

The Nash modification of an algebraic variety replaces its singular points by limits of tangent spaces at smooth points. It is an open problem whether successive Nash modification eventually resolves all singularities. This paper studies this problem for not necessarily normal toric surfaces, using the combinatorial description of Nash modification on toric varieties in [D. Yu. Grigoriev and P. D. Milman, Adv. Math. 231 (2012), no. 6, 3389–3428; MR2980503], and establishes desingularization on certain affine charts.