ANDERSSON, Mats; ERIKSSON, Dennis; KALM, Håkan Samuelsson; WULCAN, Elizabeth; YGER, Alain

doi:10.1007/s00208-020-01973-y

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ANDERSSON, Mats
Department of Mathematical Sciences
Department of Mathematical Sciences [Chalmers]

ERIKSSON, Dennis
Chalmers University of Technology [Göteborg]

KALM, Håkan Samuelsson
Chalmers University of Technology [Göteborg]

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Matematische Annalen. 2020

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2020

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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 $\mathcal{B}(X)$ 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 $\mathcal{B}$-analogues of classical intersection theoretic constructions: For an analytic subspace $V\subset X$ we define a $\mathcal{B}$-Segre class, which is an element of $\mathcal{B}(X)$ 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-Amp\`ere-type product. For regular embeddings we construct a $\mathcal{B}$-analogue of the Gysin morphism.< Réduire

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Global representation of Segre numbers by Monge-Amp\`ere products

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