Minimal plane valuations
نویسندگان
چکیده
منابع مشابه
Evaluation codes and plane valuations
We apply tools coming from singularity theory, as Hamburger-Noether expansions, and from valuation theory, as generating sequences, to explicitly describe order functions given by valuations of 2-dimensional function fields. We show that these order functions are simple when their ordered domains are isomorphic to the value semigroup algebra of the corresponding valuation. Otherwise, we provide...
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We let R be an o-minimal expansion of a field, V a convex subring, and (R0, V0) an elementary substructure of (R, V ). We let L be the language consisting of a language for R, in which R has elimination of quantifiers, and a predicate for V , and we let LR0 be the language L expanded by constants for all elements of R0. Our main result is that (R, V ) considered as an LR0-structure is model com...
متن کاملPlurisubharmonic functions on the octonionic plane and Spin ( 9 ) - invariant valuations on convex sets
A new class of plurisubharmonic functions on the octonionic plane O2 ≃ R16 is introduced. An octonionic version of theorems of A.D. Aleksandrov [3] and ChernLevine-Nirenberg [24], and B locki [21] are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of O2 ≃ R 16. In particular a new example of Spin(9)-invariant valuation o...
متن کاملEvaluation codes defined by finite families of plane valuations at infinity
We construct evaluation codes given by weight functions defined over polynomial rings in m ≥ 2 indeterminates. These weight functions are determined by sets of m− 1 weight functions over polynomial rings in two indeterminates defined by plane valuations at infinity. Well-suited families in totally ordered commutative groups are an important tool in our procedure.
متن کاملFinite families of plane valuations: value semigroup, graded algebra and Poincaré series
The formal definition of valuation was firstly given by the Hungarian mathematician J. Kürschák in 1912 supported with ideas of Hensel. Valuation theory, based on this concept, has been developed by a large number of contributors (some of them distinguished mathematicians as Krull or Zariski) and it has a wide range of applications in different context and research areas as, for instance, algeb...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2018
ISSN: 1056-3911,1534-7486
DOI: 10.1090/jag/722