### 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.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.

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.

We consider complex analytic sets with proper intersection. We find their regular separation exponent using basic notions of intersection multiplicity theory.

We give representations of Nash functions in a neighbourhood of a polydisc (torus) in ${\u2102}^{m}$ as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in ${\u2102}^{m+1}$.

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.

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.

**Page 1**