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A subring of a discrete valuation ring Rv is called an Rv-Arf ring if it satisfies a certain condition first considered by C. Arf some forty-five years ago. Let A be any subring of Rv and let I be an ideal of A. The operation of the blow up of A[...]texto impreso
We consider complete ideals supported on finite sequences of infinitely near points, in regular local rings with dimensions greater than two. We study properties of factorizations in Lipman special *-simple complete ideals. We relate it to a typ[...]texto impreso
This monograph presents a local theory of planar and space curve singularities both from an algebraic and geometric point of view, being motivated by possible extensions of the Zariski equisingularity theory to the case of space curves and by ma[...]texto impreso
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The authors use the Arf closure relative to divisorial valuations to define an extension of Puiseux exponents for general singularities. Primary exponents come from valuation associated to arc space components. Secondary exponents are related to[...]texto impreso
In this article I examine the Aristotelian definition of the human being as “political animal” in the light of the changes human condition has experienced in the last two centuries. Specifically, I make an interpretation of Aristotle based on Ar[...]texto impreso
Let k be a real closed field. A real AP-curve (over k) is a 1-dimensional, excellent Henselian local real domain with residue field k. A 1-dimensional Noetherian local ring is Arf, if emb dim(B)=mult(B) for every local ring B infinitely near to [...]texto impreso
The aim of this article is twofold. On the one hand, I will outline the diverse usages that the concept of history has taken on throughout Western history. These different usages may be grouped together in three semantic fields (history as a way[...]texto impreso
Equisingularity for plane curves can be described in terms of the Puiseux invariants (Puiseux exponents of the branches and the intersection multiplicities). For space curves, the combinatorics of the resolution process is equivalent to the Arf [...]
