Computation of topological invariants for real projective surfaces with isolated singularities

Elisabetta Fortuna (1) , Patrizia Gianni (1) , Barry Trager (2)

1 University of Pisa - Università di Pisa
2 IBM Research

Given a real algebraic surface $S$ in $\pro$, we propose a procedure to determine the topology of $S$ and to compute non-trivial topological invariants for the pair $(\pro, S)$ 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 labelled 2-adjacency graph of the surface.

Domaines: Géométrie algébrique [math.AG]

Elisabetta Fortuna, Patrizia Gianni, Barry Trager. Computation of topological invariants for real projective surfaces with isolated singularities. MEGA'2013 (Special Issue), Jun 2013, Frankfurt am Main, Allemagne. ⟨hal-01022875⟩