| 1. |
- Andersson, Mats, 1957, et al.
(författare)
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A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas
- 2012
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Ingår i: Inventiones Mathematicae. - : Springer Science and Business Media LLC. - 0020-9910 .- 1432-1297. ; 190:2, s. 261-297
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Tidskriftsartikel (refereegranskat)abstract
- Let $X$ be a complex space of pure dimension. We introduce fine sheaves $\A^X_q$ of $(0,q)$-currents, which coincides with the sheaves of smooth forms on the regular part of $X$, so that the associated Dolbeault complex yields a resolution of the structure sheaf $\hol^X$. Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.
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| 2. |
- Andersson, Mats, 1957
(författare)
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A generalized Poincare-Lelong formula
- 2007
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Ingår i: Mathematica Scandinavica. - 0025-5521 .- 1903-1807. ; 101:2, s. 195-218
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Tidskriftsartikel (refereegranskat)abstract
- We prove a generalization of the classical Poincare-Lelong formula. Given a holomorphic section f, with zero set Z, of a Hermitian vector bundle E -> X, let S be the line bundle over X\Z spanned by f and let Q = E/S. Then the Chern form c(D-Q) is locally integrable and closed in X and there is a current W such that dd(c)W = c(D-E) - c(D-Q) - M, where M is a current with support on Z. In particular, the top Bott-Chern class is represented by a current with support on Z. We discuss positivity of these currents, and we also reveal a close relation with principal value and residue currents of Cauchy-Fantappie-Leray type.
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| 3. |
- Andersson, Mats, 1957
(författare)
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A global Briançon-Skoda-Huneke-Sznajdman theorem
- 2018
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Ingår i: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 1903-1807 .- 0025-5521. ; 122:1, s. 31-52
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Tidskriftsartikel (refereegranskat)abstract
- We prove a global effective membership result for polynomials on a non-reduced algebraic sub variety of C-N. It can be seen as a global version of a recent local result of Sznajdman. generalizine the Briancon-Skoda-Huneke theorem for the local ring of holomorphic functions at a point on a reduced analytic space.
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| 4. |
- Andersson, Mats, 1957, et al.
(författare)
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A note on smooth forms on analytic spaces
- 2021
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Ingår i: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 127:3, s. 521-526
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Tidskriftsartikel (refereegranskat)abstract
- We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms.
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| 5. |
- Andersson, Mats, 1957
(författare)
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A pointwise norm on a non-reduced analytic space
- 2022
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 283:4
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Tidskriftsartikel (refereegranskat)abstract
- Let X be a possibly non-reduced space of pure dimension. We introduce a pointwise Hermitian norm on smooth (0, q)-forms, in particular on holomorphic functions, on X. The norm is canonical, up to equivalence, where the underlying reduced space is a manifold. We prove that the space of holomorphic functions is complete with respect to the natural topology induced by this norm. (C) 2022 Elsevier Inc. All rights reserved.
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| 6. |
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| 7. |
- Andersson, Mats, 1957
(författare)
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A residue criterion for strong holomorphicity
- 2010
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Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 48:1, s. 1-15
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Tidskriftsartikel (refereegranskat)abstract
- We give a local criterion in terms of a residue current for strong holomorphicity of a meromorphic function on an arbitrary pure-dimensional analytic variety. This generalizes a result by A. Tsikh for the case of a reduced complete intersection.
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| 8. |
- Andersson, Mats, 1957
(författare)
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An explicit Koppelman formula for dd(c) and Green currents on p(n)
- 2011
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 267:3-4, s. 835-850
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Tidskriftsartikel (refereegranskat)abstract
- We compute a quite explicit Koppelman formula for dd (c) on projective space, and obtain Green currents for closed (p, p)-currents.
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| 9. |
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| 10. |
- Andersson, Mats, 1957
(författare)
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Coleff-Herrera currents, duality, and Noetherian operators
- 2011
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Ingår i: Bulletin De La Societe Mathematique De France. - 0037-9484. ; 139:4, s. 535-554
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Tidskriftsartikel (refereegranskat)abstract
- Let I be a coherent subsheaf of a locally free sheaf O(E-0) and suppose that I = O(E-0)/I has pure codimension. Starting with a residue current R obtained from a locally free resolution of I we construct a. vector-valued Coleff-Herrera current it with support on the variety associated to I such that phi is in I if and only if mu phi = 0. Such a current mu can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction due to Bjork one gets Noetherian operators for I from the current mu. The current R also provides an explicit realization of the Dickenstein-Sessa decomposition and other related canonical isomorphisms.
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