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Displaying similar documents to “Spaces of polynomial functions of bounded degrees on an embedded manifold and their duals”

Holomorphic line bundles and divisors on a domain of a Stein manifold

Makoto Abe (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let D be an open set of a Stein manifold X of dimension n such that H k ( D , 𝒪 ) = 0 for 2 k n - 1 . We prove that D is Stein if and only if every topologically trivial holomorphic line bundle L on D is associated to some Cartier divisor 𝔡 on D .

Steinness of bundles with fiber a Reinhardt bounded domain

Karl Oeljeklaus, Dan Zaffran (2006)

Bulletin de la Société Mathématique de France

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Let E denote a holomorphic bundle with fiber D and with basis B . Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d = 2 or 3 , we give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1 ); for d = 2 , we give necessary and sufficient criteria for E to be Stein (Theorem 2 ). For D a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for E to be Stein (Theorem...

Augmentation quotients for Burnside rings of generalized dihedral groups

Shan Chang (2016)

Czechoslovak Mathematical Journal

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Let H be a finite abelian group of odd order, 𝒟 be its generalized dihedral group, i.e., the semidirect product of C 2 acting on H by inverting elements, where C 2 is the cyclic group of order two. Let Ω ( 𝒟 ) be the Burnside ring of 𝒟 , Δ ( 𝒟 ) be the augmentation ideal of Ω ( 𝒟 ) . Denote by Δ n ( 𝒟 ) and Q n ( 𝒟 ) the n th power of Δ ( 𝒟 ) and the n th consecutive quotient group Δ n ( 𝒟 ) / Δ n + 1 ( 𝒟 ) , respectively. This paper provides an explicit -basis for Δ n ( 𝒟 ) and determines the isomorphism class of Q n ( 𝒟 ) for each positive integer n .

Spaces of geometrically generic configurations

Yoel Feler (2008)

Journal of the European Mathematical Society

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Let X denote either ℂℙ m or m . We study certain analytic properties of the space n ( X , g p ) of ordered geometrically generic n -point configurations in X . This space consists of all q = ( q 1 , , q n ) X n such that no m + 1 of the points q 1 , , q n belong to a hyperplane in X . In particular, we show that for a big enough n any holomorphic map f : n ( ℂℙ m , g p ) n ( ℂℙ m , g p ) commuting with the natural action of the symmetric group 𝐒 ( n ) in n ( ℂℙ m , g p ) is of the form f ( q ) = τ ( q ) q = ( τ ( q ) q 1 , , τ ( q ) q n ) , q n ( ℂℙ m , g p ) , where τ : n ( ℂℙ m , g p ) 𝐏𝐒𝐋 ( m + 1 , ) is an 𝐒 ( n ) -invariant holomorphic map. A similar result holds true for mappings of the configuration...

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...

The clean elements of the ring ( L )

Ali Akbar Estaji, Maryam Taha (2024)

Czechoslovak Mathematical Journal

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We characterize clean elements of ( L ) and show that α ( L ) is clean if and only if there exists a clopen sublocale U in L such that 𝔠 L ( coz ( α - 1 ) ) U 𝔬 L ( coz ( α ) ) . Also, we prove that ( L ) is clean if and only if ( L ) has a clean prime ideal. Then, according to the results about ( L ) , we immediately get results about 𝒞 c ( L ) .

The general rigidity result for bundles of A -covelocities and A -jets

Jiří M. Tomáš (2017)

Czechoslovak Mathematical Journal

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Let M be an m -dimensional manifold and A = 𝔻 k r / I = N A a Weil algebra of height r . We prove that any A -covelocity T x A f T x A * M , x M is determined by its values over arbitrary max { width A , m } regular and under the first jet projection linearly independent elements of T x A M . Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result T A * M T r * M without coordinate computations, which improves and generalizes the partial...

A note on the multiplier ideals of monomial ideals

Cheng Gong, Zhongming Tang (2015)

Czechoslovak Mathematical Journal

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Let 𝔞 [ x 1 , ... , x n ] be a monomial ideal and 𝒥 ( 𝔞 c ) the multiplier ideal of 𝔞 with coefficient c . Then 𝒥 ( 𝔞 c ) is also a monomial ideal of [ x 1 , ... , x n ] , and the equality 𝒥 ( 𝔞 c ) = 𝔞 implies that 0 < c < n + 1 . We mainly discuss the problem when 𝒥 ( 𝔞 ) = 𝔞 or 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 for all 0 < ε < 1 . It is proved that if 𝒥 ( 𝔞 ) = 𝔞 then 𝔞 is principal, and if 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 holds for all 0 < ε < 1 then 𝔞 = ( x 1 , ... , x n ) . One global result is also obtained. Let 𝔞 ˜ be the ideal sheaf on n - 1 associated with 𝔞 . Then it is proved that the equality 𝒥 ( 𝔞 ˜ ) = 𝔞 ˜ implies that 𝔞 ˜ is principal.

On extending C k functions from an open set to with applications

Walter D. Burgess, Robert M. Raphael (2023)

Czechoslovak Mathematical Journal

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For k { } and U open in , let C k ( U ) be the ring of real valued functions on U with the first k derivatives continuous. It is shown that for f C k ( U ) there is g C ( ) with U coz g and h C k ( ) with f g | U = h | U . The function f and its k derivatives are not assumed to be bounded on U . The function g is constructed using splines based on the Mollifier function. Some consequences about the ring C k ( ) are deduced from this, in particular that Q cl ( C k ( ) ) = Q ( C k ( ) ) .

Annihilating and power-commuting generalized skew derivations on Lie ideals in prime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

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Let R be a prime ring of characteristic different from 2 and 3, Q r its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n 1 a fixed positive integer. Let α be an automorphism of the ring R . An additive map D : R R is called an α -derivation (or a skew derivation) on R if D ( x y ) = D ( x ) y + α ( x ) D ( y ) for all x , y R . An additive mapping F : R R is called a generalized α -derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F ( x y ) = F ( x ) y + α ( x ) D ( y ) for all x , y R . We prove...

Local density of diffeomorphisms with large centralizers

Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)

Annales scientifiques de l'École Normale Supérieure

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Given any compact manifold M , we construct a non-empty open subset 𝒪 of the space Diff 1 ( M ) of C 1 -diffeomorphisms and a dense subset 𝒟 𝒪 such that the centralizer of every diffeomorphism in 𝒟 is uncountable, hence non-trivial.