On The Curvature of the Real Milnor Fiber

Let C be a germ at O R² of a real analytic plane curve, andC^C its complexification; let C_t B be a fiber of a real smoothdeformation of C in the ball B = B(O,). The following inequalityis proved between the integrals of real curvature k of C_t andthose of Gaussian curvature K of : The sharpness of this inequality is proved in the case whereC is a real irreducible germ. Similar results are proved foran affine algebraic curve C R² of degree d. 2000 MathematicsSubject Classification 14H20, 14H50, 53A04.