MATHEMATICA SCANDINAVICA https://www.mscand.dk/ en-US mscand@math.au.dk (Andrew Swann) mscand@math.au.dk (Anne Mette Christiansen) Sat, 19 Oct 2019 14:53:17 +0200 OJS 3.1.1.4 http://blogs.law.harvard.edu/tech/rss 60 Free resolutions of Dynkin format and the licci property of grade $3$ perfect ideals https://www.mscand.dk/article/view/114894 <p>Recent work on generic free resolutions of length $3$ attaches to every resolution a graph and suggests that resolutions whose associated graph is a Dynkin diagram are distinguished. We conjecture that in a regular local ring, every grade $3$ perfect ideal whose minimal free resolution is distinguished in this way is in the linkage class of a complete intersection.</p> Lars Winther Christensen, Oana Veliche, Jerzy Weyman ##submission.copyrightStatement## https://www.mscand.dk/article/view/114894 Sat, 19 Oct 2019 00:00:00 +0200 Vandermonde determinantal ideals https://www.mscand.dk/article/view/114906 <p>We show that the ideal generated by maximal minors (i.e., $k+1$-minors) of a $(k+1) \times n$ Vandermonde matrix is radical and Cohen-Macaulay. Note that this ideal is generated by all Specht polynomials with shape $(n-k,1, …,1)$.</p> Junzo Watanabe, Kohji Yanagawa ##submission.copyrightStatement## https://www.mscand.dk/article/view/114906 Sat, 19 Oct 2019 00:00:00 +0200 Arrow categories of monoidal model categories https://www.mscand.dk/article/view/114968 <p>We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category. This answers a question posed by Mark Hovey, in the course of his work on Smith ideals. As a corollary, we prove that the projective model structure in cubical homotopy theory is a monoidal model structure. As illustrations we include numerous examples of non-cofibrantly generated monoidal model categories, including chain complexes, small categories, pro-categories, and topological spaces.</p> David White, Donald Yau ##submission.copyrightStatement## https://www.mscand.dk/article/view/114968 Sat, 19 Oct 2019 00:00:00 +0200 Approximation and interpolation of regular maps from affine varieties to algebraic manifolds https://www.mscand.dk/article/view/114893 <p>We consider the analogue for regular maps from affine varieties to suitable algebraic manifolds of Oka theory for holomorphic maps from Stein spaces to suitable complex manifolds. The goal is to understand when the obstructions to approximation or interpolation are purely topological. We propose a definition of an algebraic Oka property, which is stronger than the analytic Oka property. We review the known examples of algebraic manifolds satisfying the algebraic Oka property and add a new class of examples: smooth nondegenerate toric varieties. On the other hand, we show that the algebraic analogues of three of the central properties of analytic Oka theory fail for all compact manifolds and manifolds with a rational curve; in particular, for projective manifolds.</p> Finnur Lárusson, Tuyen Trung Truong ##submission.copyrightStatement## https://www.mscand.dk/article/view/114893 Sat, 19 Oct 2019 00:00:00 +0200 On diagonal quasi-free automorphisms of simple Cuntz-Krieger algebras https://www.mscand.dk/article/view/114823 <p>We show that an outer action of a finite abelian group on a simple Cuntz-Krieger algebra is strongly approximately inner in the sense of Izumi if the action is given by diagonal quasi-free automorphisms and the associated matrix is aperiodic. This is achieved by an approximate cohomology vanishing-type argument for the canonical shift restricted to the relative commutant of the set of domain projections of the canonical generating isometries in the fixed point algebra.</p> Selçuk Barlak, Gábor Szabó ##submission.copyrightStatement## https://www.mscand.dk/article/view/114823 Sat, 19 Oct 2019 00:00:00 +0200 A short note on Helmholtz decompositions for bounded domains in $\mathbb{R}^3$ https://www.mscand.dk/article/view/114908 <p>In this short note we consider several widely used $\mathsf {L}^{2}$-orthogonal Helmholtz decompositions for bounded domains in $\mathbb {R}^3$. It is well known that one part of the decompositions is a subspace of the space of functions with zero mean. We refine this global property into a local equivalent: we show that functions from these spaces have zero mean in every subdomain of specific decompositions of the domain.</p> <p>An application of the zero mean properties is presented for convex domains. We introduce a specialized Poincaré-type inequality, and estimate the related unknown constant from above. The upper bound is derived using the upper bound for the Poincaré constant proven by Payne and Weinberger. This is then used to obtain a small improvement of upper bounds of two Maxwell-type constants originally proven by Pauly.</p> <p>Although the two dimensional case is not considered, all derived results can be repeated in $\mathbb {R}^2$ by similar calculations.</p> Immanuel Anjam ##submission.copyrightStatement## https://www.mscand.dk/article/view/114908 Sat, 19 Oct 2019 00:00:00 +0200 Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I https://www.mscand.dk/article/view/114892 <p>In this paper we prove the Hardy inequalities for the quadratic form of the Laplacian with the Landau Hamiltonian type magnetic field. Moreover, we obtain a Poincaré type inequality and inequalities with more general families of weights. Furthermore, we establish weighted Hardy inequalities for the quadratic form of the magnetic Baouendi-Grushin operator for the magnetic field of Aharonov-Bohm type. For these, we show refinements of the known Hardy inequalities for the Baouendi-Grushin operator involving radial derivatives in some of the variables. The corresponding uncertainty type principles are also obtained.</p> Ari Laptev, Michael Ruzhansky, Nurgissa Yessirkegenov ##submission.copyrightStatement## https://www.mscand.dk/article/view/114892 Sat, 19 Oct 2019 00:00:00 +0200 Isomorphisms of spaces of affine continuous complex functions https://www.mscand.dk/article/view/114989 <p>Let $X$ and $Y$ be compact convex sets such that their each extreme point is a weak peak point. We show that $\operatorname{ext} X$ is homeomorphic to $\operatorname{ext} Y$ provided there exists a small-bound isomorphism of the space $\mathfrak{A}(X,\mathbb{C} )$ of continuous affine complex functions on $X$ onto $\mathfrak{A}(Y,\mathbb{C} )$. Further, we generalize a result of Cengiz to the context of compact convex sets.</p> Jakub Rondoš, Jiří Spurný ##submission.copyrightStatement## https://www.mscand.dk/article/view/114989 Sat, 19 Oct 2019 00:00:00 +0200 The Cuntz-Pimsner extension and mapping cone exact sequences https://www.mscand.dk/article/view/115634 <p>For Cuntz-Pimsner algebras of bi-Hilbertian bimodules with finite Jones-Watatani index satisfying some side conditions, we give an explicit isomorphism between the $K$-theory exact sequences of the mapping cone of the inclusion of the coefficient algebra into a Cuntz-Pimsner algebra, and the Cuntz-Pimsner exact sequence. In the process we extend some results by the second author and collaborators from finite projective bimodules to certain finite index bimodules, and also clarify some aspects of Pimsner's `extension of scalars' construction.</p> Francesca Arici, Adam Rennie ##submission.copyrightStatement## https://www.mscand.dk/article/view/115634 Sat, 19 Oct 2019 00:00:00 +0200 Volume index https://www.mscand.dk/article/view/116355 <p>Volume index</p> ##submission.copyrightStatement## https://www.mscand.dk/article/view/116355 Sat, 19 Oct 2019 00:00:00 +0200 Issue covers https://www.mscand.dk/article/view/116354 <p>Issue covers</p> ##submission.copyrightStatement## https://www.mscand.dk/article/view/116354 Sat, 19 Oct 2019 00:00:00 +0200