| 1. |
- 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.
|
|
| 2. |
|
|
| 3. |
- Andersson, Mats, 1957, et al.
(författare)
-
Nonproper intersection products and generalized cycles
- 2021
-
Ingår i: European Journal of Mathematics. - : Springer Science and Business Media LLC. - 2199-675X .- 2199-6768. ; 7:4, s. 1337-1381
-
Tidskriftsartikel (refereegranskat)abstract
- We develop intersection theory in terms of the B-group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct images of Chern forms and it contains all usual cycles. However, contrary to Chow classes, the B-classes have well-defined multiplicities at each point. We focus on a B-analogue of the intersection theory based on the Stuckrad-Vogel procedure and the join construction in projective space. Our approach provides global B-classes which satisfy a Bezout theorem and have the expected local intersection numbers. We also introduce B-analogues of more classical constructions of intersections using the Gysin map of the diagonal. These constructions are connected via a B-variant of van Gastel's formulas. Furthermore, we prove that our intersections coincide with the classical ones on cohomology level.
|
|
| 4. |
- Andersson, Mats, 1957, et al.
(författare)
-
One parameter regularizations of products of residue currents
- 2017
-
Ingår i: Trends in Mathematics. - Cham : Springer. - 2297-0215 .- 2297-024X. - 9783319524719 ; , s. 81-90
-
Bokkapitel (refereegranskat)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.
|
|
| 5. |
- Andersson, Mats, 1957, et al.
(författare)
-
Segre numbers, a generalized King formula, and local intersections
- 2017
-
Ingår i: Journal für die Reine und Angewandte Mathematik. - : Walter de Gruyter GmbH. - 1435-5345 .- 0075-4102. ; 728:728, s. 105-136
-
Tidskriftsartikel (refereegranskat)abstract
- Let $\mathcal{J}$ be an ideal sheaf on a reduced analytic space $X$ with zero set $Z$.We show that the Lelong numbers of the restrictions to $Z$ of certain generalized Monge–Ampère products $(dd^c \log |f|^2)^k$, where $f$ is a tuple of generators of $\mathcal{J}$, coincide with theso-called Segre numbers of $\mathcal{J}$, introduced independently by Tworzewski, Achilles–Manaresi,and Gaffney–Gassler. More generally we show that these currents satisfy a generalization ofthe classical King formula that takes into account fixed and moving components of Vogelcycles associated with $\mathcal{J}$. A basic tool is a new calculus for products of positive currents ofBochner–Martinelli type. We also discuss connections to intersection theory.
|
|
| 6. |
|
|
