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| 2. |
- Götmark, Elin, 1979, et al.
(author)
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Koppelman formulas on Grassmannians
- 2010
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In: Journal für die reine und angewandte Mathematik. - : Walter de Gruyter. - 0075-4102 .- 1435-5345. ; 640:(March), s. 101-115
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Journal article (peer-reviewed)abstract
- We construct Koppelman formulas on Grassmannians for forms with values in any holomorphic line bundle as well as in the tautological vector bundle and its dual. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding -equation. We also relate the projection part of our formulas to the Bergman kernels associated to the line bundles.
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| 3. |
- Samuelsson Kalm, Håkan, 1976, et al.
(author)
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Koppelman formulas on flag manifolds and harmonic forms
- 2012
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 272:3-4, s. 1087-1095
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Journal article (peer-reviewed)abstract
- We construct Koppelman formulas on manifolds of flags in for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding -equation. We also construct reproducing kernels for harmonic (p, q)-forms in the case of Grassmannians.
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| 4. |
- Andersson, Mats, 1957, et al.
(author)
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A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas
- 2012
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In: Inventiones Mathematicae. - : Springer Science and Business Media LLC. - 0020-9910 .- 1432-1297. ; 190:2, s. 261-297
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Journal article (peer-reviewed)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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| 5. |
- Andersson, Mats, 1957, et al.
(author)
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A note on smooth forms on analytic spaces
- 2021
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In: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 127:3, s. 521-526
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Journal article (peer-reviewed)abstract
- We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms.
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| 6. |
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| 7. |
- Andersson, Mats, 1957, et al.
(author)
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On non-proper intersections and local intersection numbers
- 2022
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 300:1, s. 1019-1039
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Journal article (peer-reviewed)abstract
- Given equidimensional (generalized) cycles mu(1) and mu(2) on a complex manifold Y we introduce a product mu(1) lozenge Y mu(2) that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point. If Y is projective, then given a very ample line bundle L -> Y we define a product mu(1)circle L mu(2) whose multiplicities at each point also coincide with the local intersection numbers. In addition, provided that mu(1) and mu(2) are effective, this product satisfies a Bezout inequality. If i : Y -> P-N is an embedding such that i* O(1) = L, then mu(1)circle L mu(2) can be expressed as a mean value of Stuckrad-Vogel cycles on P-N. There are quite explicit relations between lozenge Y and circle L.
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| 8. |
- Andersson, Mats, 1957, et al.
(author)
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On the Briancon-Skoda theorem on a singular variety
- 2010
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In: Annales de l'institut Fourier. - : Cellule MathDoc/CEDRAM. - 0373-0956 .- 1777-5310. ; 60:2, s. 417-432
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Journal article (peer-reviewed)abstract
- Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briancon-Skoda theorem for the local ring Oz; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.
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| 9. |
- Andersson, Mats, 1957, et al.
(author)
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One parameter regularizations of products of residue currents
- 2017
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In: Trends in Mathematics. - Cham : Springer. - 2297-0215 .- 2297-024X. - 9783319524719 ; , s. 81-90
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Book chapter (peer-reviewed)abstract
- © 2017 Springer International Publishing. We show that Coleff–Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.
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