منابع مشابه
Flag Higher Nash Blowups
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.
متن کاملHigher 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 کاملUnstable Blowups
Let (X,L) be a polarised manifold. We show that K-stability and asymptotic Chow stability of the blowup of X along a 0-dimensional cycle are closely related to Chow stability of the cycle itself, for polarizations making the exceptional divisors small. This can be used to give (almost) a converse to the results of Arezzo and Pacard in [1], [2], and to give new examples of Kähler classes with no...
متن کاملHomology Localization by Hierarchical Blowups
Topological descriptors such as the generators of homology groups are very useful in the analysis of complex data sets. It is often desired to find the smallest such generators to help localize the interesting features. One interpretation of localization utilizes a covering of the underlying space and computes generators contained within these covers. A similar construction was later used to co...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2007
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x0700276x