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- W2904208539 abstract "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 $Vsubset X$ 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-Ampere-type product. For regular embeddings we construct a $mathcal{B}$-analogue of the Gysin morphism." @default.
- W2904208539 created "2018-12-22" @default.
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- W2904208539 date "2018-12-07" @default.
- W2904208539 modified "2023-09-27" @default.
- W2904208539 title "Global representation of Segre numbers by Monge-Amp`ere products" @default.
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