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 1337-1381

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/s40879-021-00473-w

More information

Latest update

4/5/2022 5