https://www.mscand.dk/issue/feedMATHEMATICA SCANDINAVICA2023-06-05T09:27:48+02:00Arne Jensenmscand@math.au.dkOpen Journal Systemshttps://www.mscand.dk/article/view/137125Binomial edge ideals over an exterior algebra2023-04-30T13:32:14+02:00Irena Peevamscand@math.au.dk<p>We introduce the study of binomial edge ideals over an exterior algebra.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136634Linear resolutions and quasi-linearity of monomial ideals2023-03-17T11:44:57+01:00Dancheng Lumscand@math.au.dk<p>We introduce the notion of quasi-linearity and prove it is necessary for a monomial ideal to have a linear resolution and clarify all the quasi-linear monomial ideals generated in degree $2$. We also introduce the notion of a strongly linear monomial over a monomial ideal and prove that if $\mathbf {u}$ is a monomial strongly linear over $I$ then $I$ has a linear resolution (respectively is quasi-linear) if and only if $I+\mathbf {u}\mathfrak {p}$ has a linear resolution (respectively is quasi-linear). Here $\mathfrak {p}$ is any monomial prime ideal.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136499Complexity and rigidity of Ulrich modules, and some applications2023-03-13T11:03:21+01:00Souvik Deymscand@math.au.dkDipankar Ghoshmscand@math.au.dk<p>We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can be used as test modules, which detect finite homological dimensions of modules. We prove that Ulrich modules over CM local rings have maximal complexity and curvature. Various new characterizations of local rings are provided in terms of Ulrich modules. We show that every Ulrich module of dimension $s$ over a local ring is $(s+1)$-Tor-rigid-test, but not $s$−Tor-rigid in general (where $s\ge 1$). Over a deformation of a CM local ring of minimal multiplicity, we also study Tor rigidity.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136533Constructing stable vector bundles from curves with torsion normal bundle2023-03-15T13:13:51+01:00Sergio Licanicmscand@math.au.dk<p>Given a smooth irreducible curve $S$ with torsion normal bundle on a projective surface $X$, we provide a criterion for the non-emptiness of the moduli of slope stable vector bundles with prescribed Chern classes. The criterion is given in terms of the topology of the pair $(X,S)$.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136450Approximation and accumulation results of holomorphic mappings with dense image2023-03-10T10:24:31+01:00Giovanni D. Di Salvomscand@math.au.dk<p>We present four approximation theorems for manifold–valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\mathbb{C}^n$ with holomorphic embeddings with dense images. The second theorem approximates holomorphic mappings on complex manifolds with bounded images with holomorphic mappings with dense images. The last two theorems work the other way around, constructing (in different settings) sequences of holomorphic mappings (embeddings in the first one) converging to a mapping with dense image defined on a given compact minus certain points (thus in general not holomorphic).</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136741The AH conjecture for Cantor minimal dihedral systems2023-03-26T11:46:44+02:00Eduardo Scarparomscand@math.au.dk<p>The AH conjecture relates the low-dimensional homology groups of a groupoid with the abelianization of its topological full group. We show that transformation groupoids of minimal actions of the infinite dihedral group on the Cantor set satisfy this conjecture. The proof uses Kakutani–Rokhlin partitions adapted to such systems.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136656Remarks on conformal modulus in metric spaces2023-03-20T12:34:12+01:00Matthew Romneymscand@math.au.dk<p>We give an example of an Ahlfors $3$-regular, linearly locally connected metric space homeomorphic to $\mathbb {R}^3$ containing a nondegenerate continuum $E$ with zero capacity, in the sense that the conformal modulus of the set of nontrivial curves intersecting $E$ is zero. We discuss this example in relation to the quasiconformal uniformization problem for metric spaces.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/134458On principal value and standard extension of distributions2022-10-28T14:22:35+02:00Daniel Barletmscand@math.au.dk<p>For a holomorphic function $f$ on a complex manifold $\mathscr {M}$ we explain in this article that the distribution associated to $\lvert f\rvert^{2\alpha } (\textrm{Log} \lvert f\rvert^2)^q f^{-N}$ by taking the corresponding limit on the sets $\{ \lvert f\rvert \geq \varepsilon \}$ when $\varepsilon $ goes to $0$, coincides for $\Re (\alpha ) $ non negative and $q, N \in \mathbb {N}$, with the value at $\lambda = \alpha $ of the meromorphic extension of the distribution $\lvert f\rvert^{2\lambda } (\textrm{Log} \lvert f\rvert^2)^qf^{-N}$. This implies that any distribution in the $\mathcal {D}_{\mathscr {M}}$-module generated by such a distribution has the standard extension property. This implies a non $\mathcal {O}_\mathscr {M}$ torsion result for the $\mathcal {D}_{\mathscr {M}}$-module generated by such a distribution. As an application of this result we determine generators for the conjugate modules of the regular holonomic $\mathcal {D}$-modules introduced and studied in [Barlet, D., On symmetric partial differential operators, Math. Z. 302 (2022), no. 3, 1627–1655] and [Barlet, D., On partial differential operators which annihilate the roots of the universal equation of degree $k$, arXiv:2101.01895] associated to the roots of universal equation of degree $k$, $z^k + \sum _{h=1}^k (-1)^h\sigma _hz^{k-h} = 0$.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136693The Haar state on the Vaksman-Soibelman quantum spheres2023-03-23T13:02:58+01:00Max Holst Mikkelsenmscand@math.au.dkJens Kaadmscand@math.au.dk<p>In this note we present explicit formulae for the Haar state on the Vaksman-Soibelman quantum spheres. Our formulae correct various statements appearing in the literature and our proof is straightforward relying simply on properties of the modular automorphism group for the Haar state.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136662Capacities from moduli in metric measure spaces2023-03-21T13:06:33+01:00Olli Martiomscand@math.au.dk<p>The concept of capacity is an indispensable tool for analysis and path families and their moduli play a fundamental role in a metric space $X$. It is shown that the $AM_p(\Gamma )$- and $M_p(\Gamma )$-modulus create the capacities, $\mathrm {Cap}_p^{AM}(E,G)$ and $\mathrm {Cap}_p^{M}(E,G)$, respectively, where Γ is the path family connecting an arbitrary set $E \subset G$ to the complement of a bounded open set $G$. The capacities use Lipschitz functions and their upper gradients. For $p > 1$ the capacities coincide but differ for $p=1$. For $p \geq 1$ it is shown that the $\mathrm {Cap}_p^{AM}(E,G)$-capacity equals to the classical variational Dirichlet capacity of the condenser $(E,G)$ and the $\mathrm {Cap}_p^{M}(E,G)$-capacity to the $M_p(\Gamma )$-modulus.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/136539Vanishing Morrey integrability for Riesz potentials in Morrey-Orlicz spaces2023-03-16T13:43:33+01:00Yoshihiro Mizutamscand@math.au.dkTetsu Shimomuramscand@math.au.dk<p>Our aim in this paper is to establish vanishing Morrey integrability for Riesz potentials of functions in Morrey-Orlicz spaces. We discuss the size of the exceptional sets by using a capacity and Hausdorff measure. We also give Trudinger-type exponential Morrey integrability for Riesz potentials of functions in Morrey-Orlicz spaces.</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/137724Cover12023-06-04T13:20:36+02:00Covermscand@math.au.dk<p>Cover</p>2023-06-05T00:00:00+02:00Copyright (c) 2023 MATHEMATICA SCANDINAVICA