Torsion pairs and rigid objects in tubes

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs, maximal rigid objects and the bijection between them geometrically. We also give a similar geometric description in the case of the linear orientation of a Dynkin quiver of type A.Comment: 25 pages, 13 figures. Paper shortened. Minor errors correcte

A remark on Leclerc's Frobenius categories

Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that these categories admit a description as Gorenstein projective modules over an Iwanaga-Gorenstein ring of virtual dimension at most two. This is based on a Morita type result for Frobenius categories.Comment: 5 pages, extended abstract for a talk at the Workshop Homological Bonds between Commutative Algebra and Representation Theory at CRM Barcelona, February 2015, comments welcom

Subword complexes, cluster complexes, and generalized multi-associahedra

In this paper, we use subword complexes to provide a uniform approach to finite type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any nonnegative integer k, a spherical subword complex called multi-cluster complex. For k=1, we show that this subword complex is isomorphic to the cluster complex of the given type. We show that multi-cluster complexes of types A and B coincide with known simplicial complexes, namely with the simplicial complexes of multi-triangulations and centrally symmetric multi-triangulations respectively. Furthermore, we show that the multi-cluster complex is universal in the sense that every spherical subword complex can be realized as a link of a face of the multi-cluster complex.Comment: 26 pages, 3 Tables, 2 Figures; final versio

The complete ISO spectrum of NGC 6302

We present the combined Infrared Space Observatory Short-Wavelength Spectrometer and Long-Wavelength Spectrometer 2.4--197 micron spectrum of the Planetary Nebula NGC 6302 which contains in addition to strong atomic lines, a series of emission features due to solid state components. The broad wavelength coverage enables us to more accurately identify and determine the properties of both oxygen- and carbon-rich circumstellar dust. A simple model fit was made to determine the abundance and typical temperature of the amorphous silicates, enstatite and forsterite. Forsterite and enstatite do have roughly the same abundance and temperature. The origin and location of the dust in a toroidal disk around the central star are discussed.Comment: 8 pages, 4 figures, accepted by A&A. The postscriptfile can also be found at http://www.astro.uva.nl/~frankm/papers.htm