Nonproper intersection products and generalized cycles
Artikel i vetenskaplig tidskrift, 2021

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.

Analytic cycles

Nonproper intersections

Stuckrad-Vogel procedure

Currents

Monge-Ampere type product

Författare

Mats Andersson

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Dennis Eriksson

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Hakan Samuelsson Kalm

Göteborgs universitet

Elizabeth Wulcan

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Alain Yger

Université de Bordeaux

European Journal of Mathematics

2199-675X (ISSN) 2199-6768 (eISSN)

Vol. In Press

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1007/s40879-021-00473-w

Mer information

Senast uppdaterat

2021-07-08