Global representation of Segre numbers by Monge–Ampère products
Journal article, 2020

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.

Author

Mats Andersson

Chalmers, Mathematical Sciences, Algebra and geometry

Dennis Eriksson

Chalmers, Mathematical Sciences, Algebra and geometry

Håkan Samuelsson

Chalmers, Mathematical Sciences, Algebra and geometry

Elizabeth Wulcan

Chalmers, Mathematical Sciences, Algebra and geometry

Alain Yger

University of Bordeaux

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. In Press

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/s00208-020-01973-y

More information

Latest update

10/20/2020