Computation of topological invariants for real projective surfaces with isolated singularities

Given a real algebraic surface S in RP 3 , we propose a procedure to determine the topology of S and to compute non-trivial topological invariants for the pair ( RP 3 , S ) under the hypothesis that the real singularities of S are isolated. In particular, starting from an implicit equation of the surface, we compute the number of connected components of S, their Euler characteristics and the labeled 2-adjacency graph of the surface.

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