Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring

William W. Adams; Philippe Loustaunau; Victor P. Palamodov; Daniele C. Struppa

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Displaying similar documents to “Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring”

Testing flatness and computing rank of a module using syzygies

Oswaldo Lezama (2009)

Colloquium Mathematicae

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Using syzygies computed via Gröbner bases techniques, we present algorithms for testing some homological properties for submodules of the free module $A^{m}$ , where A = R[x₁,...,xₙ] and R is a Noetherian commutative ring. We will test if a given submodule M of $A^{m}$ is flat. We will also check if M is locally free of constant dimension. Moreover, we present an algorithm that computes the rank of a flat submodule M of $A^{m}$ and also an algorithm that computes the projective dimension of an arbitrary...

Levi's forms of higher codimensional submanifolds

Andrea D&#039;Agnolo, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $X ≅ C^{n}$ , let $M$ be a $C^{2}$ hypersurface of $X$ , $S$ be a $C^{2}$ submanifold of $M$ . Denote by $L_{M}$ the Levi form of $M$ at $z_{0} \in S$ . In a previous paper [3] two numbers $s^{\pm} (S, p)$ , $p \in {({\dot{T}}_{S}^{*} X)}_{z_{0}}$ are defined; for $S = M$ they are the numbers of positive and negative eigenvalues for $L_{M}$ . For $S \subset M$ , $p \in S \times_{M} \dot{T}^{*}_{S} X)$ , we show here that $s^{\pm} (S, p)$ are still the numbers of positive and negative eigenvalues for $L_{M}$ when restricted to $T_{z_{0}}^{C} S$ . Applications to the concentration in degree for microfunctions at the boundary are given.

On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in $𝐂^{n}$

Jean Erik Björk (1974)

Annales de l'institut Fourier

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Let $V$ be an algebraic variety in $C^{n}$ and when $k \geq 0$ is an integer then $Pol (V, k)$ denotes all holomorphic functions $f (z)$ on $V$ satisfying $| f (z) | \leq C_{f} (1 + | z |)^{k}$ for all $z \in V$ and some constant $C_{f}$ . We estimate the least integer $ϵ (V, k)$ such that every $f \in Pol (V, k)$ admits an extension from $V$ into $C^{n}$ by a polynomial $P (z_{1}, ..., z_{n})$ , of degree $k + ϵ (V, k)$ at most. In particular ${lim}_{k > \infty} ϵ (V, k)$ is related to cohomology groups with coefficients in coherent analytic sheaves on $V$ . The existence of the finite integer $ϵ (V, k)$ is for example an easy consequence of Kodaira’s Vanishing Theorem. ...

Birational positivity in dimension $4$

Behrouz Taji (2014)

Annales de l’institut Fourier

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In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of $Ω^{p}$ is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an $X$ provided that $X$ has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.

Module-valued functors preserving the covering dimension

Jan Spěvák (2015)

Commentationes Mathematicae Universitatis Carolinae

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We prove a general theorem about preservation of the covering dimension $dim$ by certain covariant functors that implies, among others, the following concrete results. If $G$ G is a pathwise connected...

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In this work we give a characterization of the projective invariant pseudometric $P$ , introduced by H. Wu, for a particular class of real $\mathbf{C}^{\infty}$ -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance $p$ of $P$ in open convex regular cones of $\mathbb{R}^{n}$ , endowed with the characteristic metric.

Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao, Pengju Ma (2019)

Czechoslovak Mathematical Journal

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Let $(𝒜, ℬ)$ be a complete and hereditary cotorsion pair in the category of left $R$ -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair $(𝒜, ℬ)$ are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair $(𝒜, ℬ)$ . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion...

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Finitistic dimension and restricted injective dimension

Dejun Wu (2015)

Czechoslovak Mathematical Journal

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We study the relations between finitistic dimensions and restricted injective dimensions. Let $R$ be a ring and $T$ a left $R$ -module with $A = {End}_{R} T$ . If $_{R} T$ is selforthogonal, then we show that $rid (T_{A}) \leq findim (A_{A}) \leq findim (_{R} T) + rid (T_{A})$ . Moreover, if $R$ is a left noetherian ring and $T$ is a finitely generated left $R$ -module with finite injective dimension, then $rid (T_{A}) \leq findim (A_{A}) \leq fin . inj . \dim (_{R} R) + rid (T_{A})$ . Also we show by an example that the restricted injective dimensions of a module may be strictly smaller than the Gorenstein injective dimension.