Flag Higher Nash Blowups
نویسنده
چکیده
In his previous paper [5], the author has defined a higher version of the Nash blowup and considered it a possible candidate for the one-step resolution. In this paper, we will introduce another higher version of the Nash blowup and prove that it is compatible with products and smooth morphisms. We will also prove that the product of curves can be desingularized via both versions.
منابع مشابه
Higher Nash Blowups
For each non-negative integer n, we define the n-th Nash blowup of an algebraic variety, and call them all higher Nash blowups. When n = 1, it coincides with the classical Nash blowup. We prove that sufficiently high Nash blowups separate analytic branches. We also determine for a monomial curve in characteristic zero when its higher Nash blowups are smooth.
متن کاملResolving Toric Varieties with Nash Blowups
Let X be a variety over an algebraically closed field K . Its Nash blow-up is a variety over K with a projective morphism to X , which is an isomorphism over the smooth locus. Roughly speaking, it parametrizes all limits of tangent planes to X (a precise definition is given in §2 below). The Nash blow-up of a singular X is not always smooth but seems, in some sense, to be less singular than X ....
متن کاملSeven short stories on blowups and resolutions
The lectures adress to students and geometers who are not experts in the field, but who need to use blowups occasionally or who just want to have a good comprehension of them. References are scattered in the literature and mostly concentrate on only part of the story. This text is neither complete, but hints at least at the variety of properties, results and techniques which are related to blow...
متن کاملar X iv : 0 90 5 . 45 11 v 1 [ m at h . A G ] 2 8 M ay 2 00 9 BLOWUPS IN TAME MONOMIAL IDEALS
We study blowups of affine n-space with center an arbitrary monomial ideal and call monomial ideals that render smooth blowups tame ideals. We give a combinatorial criterion to decide whether the blowup is smooth and apply this criterion to discuss a smoothing procedure proposed by Rosenberg, monomial building sets and permutohedra.
متن کاملGross-hacking-keel I
Examples 1.1. • Y ∼= P, D a nodal cubic. • Y a complete nonsingular toric surface, D the toric boundary (i.e, the complement of the big torus orbit Gm). • Blowups: Given a Looijenga pair (Y ,D), we can take “toric blowups,” where Y is the blowup of Y at a nodal point of D and D is the inverse image of D). Note that toric blowups do not change U . “non-toric blowups,” where Ỹ is the blowup of Y ...
متن کامل