| 1. |
- Andersson, Mats, 1957, et al.
(författare)
-
Decomposition of Residue Currents
- 2010
-
Ingår i: J reine angew Math. ; 638, s. 103-118
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
|
|
| 2. |
- Andersson, Mats, 1957, et al.
(författare)
-
Direct images of semi-meromorphic currents
- 2014
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We introduce a calculus for direct images of semi-meromorphic currents. We also provide results on the behaviour of these currents under the action of holomorphic differential operators and interior multiplication by holomorphic vector fields.
|
|
| 3. |
- Andersson, Mats, 1957, et al.
(författare)
-
Direct images of semi-meromorphic currents : Images directes de courants semi-méromorphes
- 2018
-
Ingår i: Annales de l'Institut Fourier. - : Cellule MathDoc/CEDRAM. - 0373-0956 .- 1777-5310. ; 68:2, s. 875-900
-
Tidskriftsartikel (refereegranskat)abstract
- We introduce a calculus for the class $ASM(X)$ of direct images of semi-meromorphic currents on a reduded analytic space $X$, that extends the classical calculus due to Coleff, Herrera and Passare. Our main result is that each element in this class acts as a kind of multiplication on the sheaf $\mathcal{PM}_X$ of pseudomeromorphic currents on $X$. We also prove that $ASM(X)$ as well as $\mathcal{PM}_X$ and certain subsheaves are closed under the action of holomorphic differential operators and interior multiplication by holomorphic vector fields.
|
|
| 4. |
- Andersson, Mats, 1957, et al.
(författare)
-
Direct images of semi-meromorphic currents
- 2018
-
Ingår i: Annales de lInstitut Fourier. - : Cellule MathDoc/CEDRAM. - 0373-0956 .- 1777-5310. ; 68:2, s. 875-890
-
Tidskriftsartikel (refereegranskat)abstract
- We introduce a calculus for the class ASM(X) of direct images of semi-meromorphic currents on a reduded analytic space X, that extends the classical calculus due to Coleff, Herrera and Passare. Our main result is that each element in this class acts as a kind of multiplication on the sheaf PMX of pseudomeromorphic currents on X. We also prove that ASM(X) as well as PMX and certain subsheaves are closed under the action of holomorphic differential operators and interior multiplication by holomorphic vector fields.
|
|
| 5. |
- Andersson, Mats, 1957, et al.
(författare)
-
Estimates for the ∂¯ -Equation on Canonical Surfaces
- 2020
-
Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 30:3, s. 2974-3001
-
Tidskriftsartikel (refereegranskat)abstract
- We study the solvability in Lp of the ∂¯ -equation in a neighborhood of a canonical singularity on a complex surface, a so-called du Val singularity. We get a quite complete picture in case p= 2 for two natural closed extensions ∂¯ s and ∂¯ w of ∂¯. For ∂¯ s we have solvability, whereas for ∂¯ w there is solvability if and only if a certain boundary condition (∗) is fulfilled at the singularity. Our main tool is certain integral operators for solving ∂¯ introduced by the first and fourth author, and we study mapping properties of these operators at the singularity.
|
|
| 6. |
- Andersson, Mats, 1957, et al.
(författare)
-
Global effective versions of the Briancon-Skoda-Huneke theorem
- 2015
-
Ingår i: Inventiones Mathematicae. - : Springer Science and Business Media LLC. - 0020-9910 .- 1432-1297. ; 200:2, s. 607-651
-
Tidskriftsartikel (refereegranskat)abstract
- We prove global effective versions of the Briançon–Skoda–Huneke theorem. Our results extend, to singular varieties, a result of Hickel on the membership problem in polynomial ideals in Cn, and a related theorem of Ein and Lazarsfeld for smooth projective varieties. The proofs rely on known geometric estimates and new results on multivariable residue calculus.
|
|
| 7. |
- Andersson, Mats, 1957, et al.
(författare)
-
Global representation of Segre numbers by Monge–Ampère products
- 2021
-
Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 380:1-2, s. 349-391
-
Tidskriftsartikel (refereegranskat)abstract
- On a reduced analytic space X we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient B(X) that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties. We provide many B-analogues of classical intersection theoretic constructions: For an analytic subspace V⊂ X we define a B-Segre class, which is an element of B(X) with support in V. It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of V. When V is cut out by a section of a vector bundle we interpret this class as a Monge–Ampère-type product. For regular embeddings we construct a B-analogue of the Gysin morphism.
|
|
| 8. |
- Andersson, Mats, 1957, et al.
(författare)
-
Green functions, Segre numbers, and King’s formula
- 2014
-
Ingår i: Annales de lInstitut Fourier. - : Cellule MathDoc/CEDRAM. - 0373-0956 .- 1777-5310. ; 64:6, s. 2639-2657
-
Tidskriftsartikel (refereegranskat)abstract
- Let ? be a coherent ideal sheaf on a complex manifold X with zero set Z, and let G be a plurisubharmonic function such that G=log|f|+?(1) locally at Z, where f is a tuple of holomorphic functions that defines ?. We give a meaning to the Monge-Ampère products (dd c G) k for k=0,1,2,..., and prove that the Lelong numbers of the currents M k ? :=1 Z (dd c G) k at x coincide with the so-called Segre numbers of J at x, introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that M k ? satisfy a certain generalization of the classical King formula.
|
|
| 9. |
|
|
| 10. |
|
|
