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2019-01-21  23:52 hrs.

Characteristic Points, Fractional Monodromy and Euler Characteristic of Smooth Real Surfaces

Ricardo Uribe-Vargas
Université de Bourgogne


We define local invariants of three kinds of characteristic points on generic surfaces in projective 3-space or in $\mathbb{R}^3$. Our formulas for global counting of these invariants on the surface (and on domains in it) involve the Euler characteristic of the surface (and of those domains) and impose restrictions to the possible numbers of coexisting characteristic points of different types.

There is an intrinsic (fundamental) cubic form on the surface. The zeros of this form define some fields of lines tangent to the surface; these foelds degenerate at the caracteristic points. Tourning around a caracteristic point, the monodromy of these fields is fractional, but the sum of these fractions over all caracteristic points of the surface provides the Euler characteristic of the surface.



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