Displaying similar documents to “Relative subanalytic sheaves”

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

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In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second,...

Involutivity of truncated microsupports

Masaki Kashiwara, Térésa Monteiro Fernandes, Pierre Schapira (2003)

Bulletin de la Société Mathématique de France

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Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf F on a real manifold and k , if two functions vanish on SS k ( F ) , then so does their Poisson bracket.

Coleff-Herrera currents, duality, and noetherian operators

Mats Andersson (2011)

Bulletin de la Société Mathématique de France

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Let be a coherent subsheaf of a locally free sheaf 𝒪 ( E 0 ) and suppose that = 𝒪 ( E 0 ) / has pure codimension. Starting with a residue current R obtained from a locally free resolution of we construct a vector-valued Coleff-Herrera current μ with support on the variety associated to such that φ is in if and only if μ φ = 0 . Such a current μ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed....

A pure smoothness condition for Radó’s theorem for α -analytic functions

Abtin Daghighi, Frank Wikström (2016)

Czechoslovak Mathematical Journal

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Let Ω n be a bounded, simply connected -convex domain. Let α + n and let f be a function on Ω which is separately C 2 α j - 1 -smooth with respect to z j (by which we mean jointly C 2 α j - 1 -smooth with respect to Re z j , Im z j ). If f is α -analytic on Ω f - 1 ( 0 ) , then f is α -analytic on Ω . The result is well-known for the case α i = 1 , 1 i n , even when f a priori is only known to be continuous.

The "Full Clarkson-Erdős-Schwartz Theorem" on the closure of non-dense Müntz spaces

Tamás Erdélyi (2003)

Studia Mathematica

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Denote by spanf₁,f₂,... the collection of all finite linear combinations of the functions f₁,f₂,... over ℝ. The principal result of the paper is the following. Theorem (Full Clarkson-Erdős-Schwartz Theorem). Suppose ( λ j ) j = 1 is a sequence of distinct positive numbers. Then s p a n 1 , x λ , x λ , . . . is dense in C[0,1] if and only if j = 1 ( λ j ) / ( λ j ² + 1 ) = . Moreover, if j = 1 ( λ j ) / ( λ j ² + 1 ) < , then every function from the C[0,1] closure of s p a n 1 , x λ , x λ , . . . can be represented as an analytic function on z ∈ ℂ ∖ (-∞, 0]: |z| < 1 restricted to (0,1). This result improves an...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Green functions, Segre numbers, and King’s formula

Mats Andersson, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

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Let 𝒥 be a coherent ideal sheaf on a complex manifold X with zero set Z , and let G be a plurisubharmonic function such that G = log | f | + 𝒪 ( 1 ) locally at Z , where f is a tuple of holomorphic functions that defines 𝒥 . We give a meaning to the Monge-Ampère products ( d d c G ) k for k = 0 , 1 , 2 , ... , and prove that the Lelong numbers of the currents M k 𝒥 : = 1 Z ( d d c G ) k at x coincide with the so-called Segre numbers of J at x , introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that M k 𝒥 satisfy a certain...

Stable tubes in extriangulated categories

Li Wang, Jiaqun Wei, Haicheng Zhang (2022)

Czechoslovak Mathematical Journal

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Let 𝒳 be a semibrick in an extriangulated category. If 𝒳 is a τ -semibrick, then the Auslander-Reiten quiver Γ ( ( 𝒳 ) ) of the filtration subcategory ( 𝒳 ) generated by 𝒳 is 𝔸 . If 𝒳 = { X i } i = 1 t is a τ -cycle semibrick, then Γ ( ( 𝒳 ) ) is 𝔸 / τ 𝔸 t .

On coverings of simple abelian varieties

Olivier Debarre (2006)

Bulletin de la Société Mathématique de France

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To any finite covering f : Y X of degree d between smooth complex projective manifolds, one associates a vector bundle E f of rank d - 1 on X whose total space contains Y . It is known that E f is ample when X is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when X is a simple abelian variety and f does not factor through any nontrivial isogeny X ' X . This result is obtained by showing that E f is M -regular...

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

Involutivity degree of a distribution at superdensity points of its tangencies

Silvano Delladio (2021)

Archivum Mathematicum

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Let Φ 1 , ... , Φ k + 1 (with k 1 ) be vector fields of class C k in an open set U N + m , let 𝕄 be a N -dimensional C k submanifold of U and define 𝕋 : = { z 𝕄 : Φ 1 ( z ) , ... , Φ k + 1 ( z ) T z 𝕄 } where T z 𝕄 is the tangent space to 𝕄 at z . Then we expect the following property, which is obvious in the special case when z 0 is an interior point (relative to 𝕄 ) of 𝕋 : If z 0 𝕄 is a ( N + k ) -density point (relative to 𝕄 ) of 𝕋 then all the iterated Lie brackets of order less or equal to k Φ i 1 ( z 0 ) , [ Φ i 1 , Φ i 2 ] ( z 0 ) , [ [ Φ i 1 , Φ i 2 ] , Φ i 3 ] ( z 0 ) , ... ( h , i h k + 1 ) belong to T z 0 𝕄 . Such a property has been proved in [9] for k = 1 and its proof in the...

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring (2014)

Annales de l’institut Fourier

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Let X be a normal projective variety, and let A be an ample Cartier divisor on X . Suppose that X is not the projective space. We prove that the twisted cotangent sheaf Ω X A is generically nef with respect to the polarisation  A . As an application we prove a Kobayashi-Ochiai theorem for foliations: if T X is a foliation such that det i A , then i is at most the rank of .