scholarly journals Spaltenstein varieties of pure dimension

2019 ◽  
Vol 148 (1) ◽  
pp. 133-144
Author(s):  
Yiqiang Li
Keyword(s):  
Pure Dimension

Higher Order Tangents to Analytic Varieties along Curves

2003 ◽  
Vol 55 (1) ◽  
pp. 64-90 ◽  
Author(s):  
Rüdiger W. Braun ◽  
Reinhold Meise ◽  
B. A. Taylor
Keyword(s):  
Differential Operators ◽  
Necessary Conditions ◽  
Forthcoming Paper ◽  
Puiseux Series ◽  
Open Set ◽  
Partial Differential Operators ◽  
Real Analytic Functions ◽  
Pure Dimension ◽  
Analytic Varieties ◽  
Real Analytic

AbstractLet V be an analytic variety in some open set in which contains the origin and which is purely k-dimensional. For a curve γ in , defined by a convergent Puiseux series and satisfying γ(0) = 0, and d ≥ 1, define Vt := t−d(V − (t)). Then the currents defined by Vt converge to a limit current Tγ,d[V] as t tends to zero. Tγ,d[V] is either zero or its support is an algebraic variety of pure dimension k in . Properties of such limit currents and examples are presented. These results will be applied in a forthcoming paper to derive necessary conditions for varieties satisfying the local Phragmén-Lindelöf condition that was used by Hörmander to characterize the constant coefficient partial differential operators which act surjectively on the space of all real analytic functions on .

The pure dimension of rings and modules

1982 ◽  
Vol 37 (5) ◽  
pp. 170-171
Author(s):  
S N Fedin
Keyword(s):  
Pure Dimension

scholarly journals Comparison of Poisson structures on moduli spaces

2021 ◽  
Author(s):  
Indranil Biswas ◽  
Francesco Bottacin ◽  
Tomás L. Gómez
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Poisson Structures ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Algebraic Vector ◽  
Pure Dimension ◽  
Stable Sheaves ◽  
Fixed Rank ◽  
Dimension One

AbstractLet X be a complex irreducible smooth projective curve, and let $${{\mathbb {L}}}$$ L be an algebraic line bundle on X with a nonzero section $$\sigma _0$$ σ 0 . Let $${\mathcal {M}}$$ M denote the moduli space of stable Hitchin pairs $$(E,\, \theta )$$ ( E , θ ) , where E is an algebraic vector bundle on X of fixed rank r and degree $$\delta $$ δ , and $$\theta \, \in \, H^0(X,\, {\mathcal {E}nd}(E)\otimes K_X\otimes {{\mathbb {L}}})$$ θ ∈ H 0 ( X , E n d ( E ) ⊗ K X ⊗ L ) . Associating to every stable Hitchin pair its spectral data, an isomorphism of $${\mathcal {M}}$$ M with a moduli space $${\mathcal {P}}$$ P of stable sheaves of pure dimension one on the total space of $$K_X\otimes {{\mathbb {L}}}$$ K X ⊗ L is obtained. Both the moduli spaces $${\mathcal {P}}$$ P and $${\mathcal {M}}$$ M are equipped with algebraic Poisson structures, which are constructed using $$\sigma _0$$ σ 0 . Here we prove that the above isomorphism between $${\mathcal {P}}$$ P and $${\mathcal {M}}$$ M preserves the Poisson structures.

scholarly journals Strong disk property for domains in open Riemann surfaces

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1711-1716
Author(s):  
Makoto Abe ◽  
Gou Nakamura
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Approximation Property ◽  
Stein Space ◽  
Open Riemann Surface ◽  
Holomorphic Approximation ◽  
Open Set ◽  
Pure Dimension

We study the relation between the holomorphic approximation property and the strong disk property for an open set of an open Riemann surface or a Stein space of pure dimension 1.

Absolute Purity

1975 ◽  
Vol 27 (1) ◽  
pp. 6-10 ◽  
Author(s):  
David J. Fieldhouse
Keyword(s):  
Finitely Generated ◽  
Pure Dimension

Throughout this paper we use the Bourbaki [1] conventions for rings and modules: all rings are associative but not necessarily commutative and have a 1; all modules are unital.Our purpose is to extend and simplify some recent results of Maddox [7], Megibben [8], Enochs [3], and the author [5] on absolutely pure modules by introducing several new dimensions, and using the absolutely pure dimension introduced by the author in [6], This completes some work on character modules and dimension in [5] and [6].An A -module will be called an FFR-module if and only if it has a resolution by finitely generated free A -modules.

scholarly journals Pure dimension and projectivity of tropical polytopes

2016 ◽  
Vol 303 ◽  
pp. 1236-1263 ◽  
Author(s):  
Zur Izhakian ◽  
Marianne Johnson ◽  
Mark Kambites
Keyword(s):  
Pure Dimension ◽  
Tropical Polytopes

scholarly journals Defining integer-valued functions in rings of continuous definable functions over a topological field

2020 ◽  
Vol 20 (03) ◽  
pp. 2050014
Author(s):  
Luck Darnière ◽  
Marcus Tressl
Keyword(s):  
Definable Set ◽  
Ordered Field ◽  
Dimension Formula ◽  
Valued Field ◽  
Pure Dimension ◽  
Isolated Points ◽  
Topological Field ◽  
Structure Formula ◽  
Definable Functions ◽  
Ring Of Functions

Let [Formula: see text] be an expansion of either an ordered field [Formula: see text], or a valued field [Formula: see text]. Given a definable set [Formula: see text] let [Formula: see text] be the ring of continuous definable functions from [Formula: see text] to [Formula: see text]. Under very mild assumptions on the geometry of [Formula: see text] and on the structure [Formula: see text], in particular when [Formula: see text] is [Formula: see text]-minimal or [Formula: see text]-minimal, or an expansion of a local field, we prove that the ring of integers [Formula: see text] is interpretable in [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] is definably connected of pure dimension [Formula: see text], then [Formula: see text] defines the subring [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] has no isolated points, then there is a discrete ring [Formula: see text] contained in [Formula: see text] and naturally isomorphic to [Formula: see text], such that the ring of functions [Formula: see text] which take values in [Formula: see text] is definable in [Formula: see text].

scholarly journals Singular loci of instanton sheaves on projective space

2016 ◽  
Vol 27 (07) ◽  
pp. 1640006 ◽  
Author(s):  
Michael Gargate ◽  
Marcos Jardim
Keyword(s):  
Projective Space ◽  
Singular Locus ◽  
Dimension Formula ◽  
Pure Dimension ◽  
Singular Loci ◽  
Higher Rank

We prove that the singular locus of a rank [Formula: see text] non-locally free instanton sheaf [Formula: see text] on [Formula: see text] has pure dimension [Formula: see text]. Moreover, we also show that the dual and double dual of [Formula: see text] are isomorphic locally free instanton sheaves, and that the sheaves [Formula: see text] and [Formula: see text] are rank [Formula: see text] instantons. We also provide explicit examples of instanton sheaves of ranks [Formula: see text] and [Formula: see text] illustrating that all of these claims are false for higher rank instanton sheaves.

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