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Abstract:
Algebraic geometers study curves, surfaces, and higher dimensional objects
that are defined implicitly by systems of polynomial equations.
Manipulating polynomial equations on a computer can reveal interesting
geometric properties of their solution sets. The Mayr-Meyer examples show
that such computations can be very costly in general. However, in "nice"
geometric situations, computations are often quite manageable.
Recent work shows that the "complexity" of computing lexicographically
with a curve in generic coordinates is governed by the singularities of a
generic projection. I will discuss joint work with Aldo Conca treating a
special case of this phenomenon and remark upon the general situation.
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