Arnolds' seminar
October 16, 2001.

Adriana Ortiz-Rodriguez (Paris 7)
On the special parabolic points and the topology of the
parabolic curve of certain smooth surfaces in $R^3$.

We consider a smooth surface in the real 3-space which is the
graph of a polynomial of the form $f=\ell_1 \cdot\ldots\cdot \ell_n$,
where $\ell_i$ are generic affine functions on the plane. For such  
a surface not having flat umbilic points, we give upper and lower 
bounds for the number of compact connected components of the parabolic
curve and a lower bound for the number of special parabolic points.