Abstract:
We explore the relation between the topology of the fibers of a
polynomial in two complex variables and the degree of the associated
discriminant. This gives, in particular, lower and
upper bounds for this degree, and the polynomials realizing these
bounds, or even close values, can be described geometrically, see
Theorems 3.1, 3.2, 3.3 and 3.4.
Key Words: Plane curves, polar curves, discriminant.
2000 Mathematics Subject Classification: Primary: 14H50;
Secondary: 14H20,
32S15.
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