Nonproper intersection products and generalized cycles
Journal article, 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
Author
Mats Andersson
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Dennis Eriksson
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Håkan Samuelsson
Chalmers, Mathematical Sciences, Algebra and geometry
University of Gothenburg
Elizabeth Wulcan
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Chalmers, Mathematical Sciences
Alain Yger
University of Bordeaux
European Journal of Mathematics
2199-675X (ISSN) 2199-6768 (eISSN)
Vol. 7 4 1337-1381Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.1007/s40879-021-00473-w