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.
Currents
Analytic cycles
Nonproper intersections
Stuckrad-Vogel procedure
Monge-Ampere type product
Författare
Mats Andersson
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Algebra och geometri
Dennis Eriksson
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Algebra och geometri
Håkan Samuelsson
Chalmers, Matematiska vetenskaper, Algebra och geometri
Göteborgs universitet
Elizabeth Wulcan
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Algebra och geometri
Chalmers, Matematiska vetenskaper
Alain Yger
Université de Bordeaux
European Journal of Mathematics
2199-675X (ISSN) 2199-6768 (eISSN)
Vol. 7 4 1337-1381Ämneskategorier
Algebra och logik
Geometri
Matematisk analys
DOI
10.1007/s40879-021-00473-w