An exact sequence of weighted Nash complexes (Q733336)

The general setting of this article is the one of three-dimensional complex algebraic varieties with isolated singularities for which a resolution of singularities \(\pi:(\tilde{U},E) \to (U,u)\) satisfying additional conditions is known. In this situation, the object of interest of the author is the generalized Nash sheaf which arises, when \(\pi\) factors through a Nash blowup \(\hat{U} \to U\) and the Nash sheaf on \(\hat{U}\) is pulled back to \(\tilde{U}\). In a previous article, the author gave a very explicit description of this situation which she uses in the present article to extend a known result from the two-dimensional case about an exact sequence expressing the Nash sheaf in terms of resolution data. The key to this generalization is the careful choice of a transversal hyperplane which makes use of technical results from Hironaka's famous 1964 desingularization article [\textit{H. Hironaka}, Ann. Math. (2) 79, 109--203, 205--326 (1964; Zbl 0122.38603)].