Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global representation of Segre numbers by Monge-Amp\`ere products   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.

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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: math-ph