Intersection theory in complex analytic geometry
We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.
Isolated intersection multiplicity and regular separation of analytic sets
An isolated point of intersection of two analytic sets is considered. We give a sharp estimate of their regular separation exponent in terms of intersection multiplicity and local degrees.
Intersections of analytic sets with linear subspaces
Proper intersection multiplicity and regular separation of analytic sets
We consider complex analytic sets with proper intersection. We find their regular separation exponent using basic notions of intersection multiplicity theory.
Diagonal series of rational functions (several variables)
We give representations of Nash functions in a neighbourhood of a polydisc (torus) in as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in .
Diagonal series of rational functions
Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.
A note on holomorphic mappings with two fixed points
A note on Bézout's theorem
We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.
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