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Algebra, Geometry, and Mathematical Physics 2010
- 2012
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Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6596 .- 1742-6588.
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Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- This proceedings volume presents results obtained by the participants of the 6th Baltic–Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25–30, 2010. The Baltic–Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic–Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic–Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers.
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| 2. |
- Berman, Robert, 1976, et al.
(författare)
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Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs
- 2014
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Ingår i: Geometric and Functional Analysis. - : Springer Science and Business Media LLC. - 1016-443X .- 1420-8970. ; 24:6, s. 1683-1730
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Tidskriftsartikel (refereegranskat)abstract
- Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical class KXdefines an ample (Formula presented.)-line bundle, and satisfying the conditions G1and S2. Our main result says that X admits a Kähler–Einstein metric iff X has semi-log canonical singularities i.e. iff X is a stable variety in the sense of Kollár–Shepherd-Barron and Alexeev (whose moduli spaces are known to be compact). By definition a Kähler–Einstein metric in this singular context simply means a Kähler–Einstein on the regular locus of X with volume equal to the algebraic volume of KX, i.e. the top intersection number of KX. We also show that such a metric is uniquely determined and extends to define a canonical positive current in c1(KX). Combined with recent results of Odaka our main result shows that X admits a Kähler–Einstein metric iff X is K-stable, which thus confirms the Yau–Tian–Donaldson conjecture in this general setting of (possibly singular) canonically polarized varieties. More generally, our results are shown to hold in the setting of log minimal varieties and they also generalize some prior results concerning Kähler–Einstein metrics on quasi-projective varieties.
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| 3. |
- Goffeng, Magnus C H T, 1987
(författare)
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Index formulas and charge deficiencies on the Landau levels
- 2010
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 51:2
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Tidskriftsartikel (refereegranskat)abstract
- The notion of charge deficiency by Avron et al. [“Charge deficiency, charge transport and comparison of dimensions,” Commun. Math. Phys. 159, 399 (1994) ] is studied from the view of K-theory of operator algebras and is applied to the Landau levels in \R^{2n}. We calculate the charge deficiencies at the higher Landau levels in \R^{2n} by means of an Atiyah–Singer-type index theorem.
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| 4. |
- Lärkäng, Richard, 1985, et al.
(författare)
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Computing residue currents of monomial ideals using comparison formulas
- 2014
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Ingår i: Bulletin des Sciences Mathématiques. - : Elsevier BV. - 0007-4497. ; 138:3, s. 376-392
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Tidskriftsartikel (refereegranskat)abstract
- Given a free resolution of an ideal a of holomorphic functions, one can construct a vector-valued residue current R, which coincides with the classical Coleff–Herrera product if a is a complete intersection ideal and whose annihilator ideal is precisely a. We give a complete description of R in the case when a is an Artinian monomial ideal and the resolution is the hull resolution (or a more general cellular resolution). The main ingredient in the proof is a comparison formula for residue currents due to the first author. By means of this description, we obtain in the monomial case a current version of a factorization of the fundamental cycle of a due to Lejeune-Jalabert.
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| 5. |
- Raufi, Hossein, 1983
(författare)
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Positive vector bundles in complex and convex geometry
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns various aspects of the geometry of holomorphic vector bundles and their analytical theory which all, vaguely speaking, are related to the notion of positive curvature in general, and L^2-methods for the dbar-equation in particular. The thesis contains four papers.In Paper I we introduce and study the notion of singular hermitian metrics on holomorphic vector bundles. We define what it means for such metrics to be positively curved in the sense of Griffiths, and investigate the assumptions needed in order to define the curvature tensor of such metrics as currents with measure coefficients. We also investigate the regularisation of such metrics.In Paper II we prove the Nakano vanishing theorem with Hörmander L^2-estimates on a compact Kähler manifold using Siu's d-dbar-Bochner-Kodaira method. We then introduce the singular hermitian metrics and regularisation results of Paper I, and use these to prove a Demailly-Nadel type of vanishing theorem for vector bundles over Riemann surfaces.A fundamental tool in complex geometry closely related to the notion of positivity is the Ohsawa-Takegoshi extension theorem. In Paper III the d-dbar-Bochner-Kodaira method is applied to extend this theorem from line bundles to vector bundles over compact Kähler manifolds. Another way of obtaining a vector bundle version of this theorem is to reduce it to the line bundle setting through the useful algebraic geometric procedure of studying the projective bundle associated with the vector bundle. In Paper III we also investigate the relationship between these two different approaches.On a trivial line bundle, a positively curved metric is the complex-analytic counterpart of a log concave function in the real-variable setting. In Paper IV we extend this link between complex and convex geometry to trivial vector bundles. We define two new notions of log concavity for real, matrix-valued functions, corresponding to Griffiths and Nakano positivity, and we prove a matrix-valued Prekopa theorem.
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| 6. |
- Samuelsson Kalm, Håkan, 1976, et al.
(författare)
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Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L^2-cohomology classes
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In the present paper, we derive an adjunction formula for the Grauert-Riemenschneider canonical sheaf of a singular hypersurface V in a complex manifold M. This adjunction formula is used to study the problem of extending L2-cohomology classes of dbar-closed forms from the singular hypersurface V to the manifold M in the spirit of the Ohsawa-Takegoshi-Manivel extension theorem. We do that by showing that our formulation of the L2-extension problem is invariant under bimeromorphic modifications, so that we can reduce the problem to the smooth case by use of an embedded resolution of V in M. The smooth case has recently been studied by Berndtsson.
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| 7. |
- Samuelsson Kalm, Håkan, 1976, et al.
(författare)
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Presence or absence of analytic structure in maximal ideal spaces
- 2014
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We study extensions of Wermer's maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no analytic disks. We answer a question posed by Lee Stout concerning the existence of analytic structure for a uniform algebra whose maximal ideal space is a manifold.
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| 8. |
- Samuelsson Kalm, Håkan, 1976, et al.
(författare)
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Regularizations of residue currents
- 2010
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Ingår i: Journal für die Reine und Angewandte Mathematik. - 1435-5345 .- 0075-4102. ; 649, s. 33-54
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Tidskriftsartikel (refereegranskat)abstract
- Under assumptions about complete intersection, we prove that Coleff-Herrera type currents satisfy a robust calculus in the sense that natural regularizations of such currents can be multiplied to yield regularizations of the Coleff-Herrera product of the currents.
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| 9. |
- Samuelsson Kalm, Håkan, 1976, et al.
(författare)
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Uniform algebras and approximation on manifolds
- 2012
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Ingår i: Inventiones Mathematicae. - : Springer Science and Business Media LLC. - 0020-9910 .- 1432-1297. ; 188:3, s. 505-523
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω⊂Cn be a bounded domain and let A⊂C(Ω¯) be a uniform algebra generated by a set F of holomorphic and pluriharmonic functions. Under natural assumptions on Ω and F we show that the only obstruction to A=C(Ω¯) is that there is a holomorphic disk D⊂Ω¯ such that all functions in F are holomorphic on D, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguished boundary of the) bidisk.
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| 10. |
- Tkachev, Vladimir
(författare)
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Minimal cubic cones via Clifford algebras
- 2010
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Ingår i: Complex Analysis and Operator Theory. - : SP Birkhäuser Verlag Basel. - 1661-8254 .- 1661-8262. ; 4:3, s. 685-700
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we construct two infinite families of algebraic minimal cones in R n . The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any n ≥ 4, n ≠ 16k + 1, there is at least one minimal cone in R n given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in R m 2 , m ≥ 2, defined by an irreducible homogeneous polynomial of degree m. These examples provide particular answers to the questions on algebraic minimal cones in R n posed by Wu-Yi Hsiang in the 1960s.
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