Real algebraic surfaces with isolated singularities

Given a real algebraic surface S in RP3, we propose a constructive procedure to determine the topology of S and to compute non-trivial topological invariants for the pair (RP3, 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 weighted 2-adjacency graph of the surface

Effective methods to compute the topology of real algebraic surfaces with isolated singularities

Given a real algebraic surface S in RP3, we propose a constructive procedure to determine the topology of S and to compute non-trivial topological invariants for the pair (RP3, 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 weighted 2-adjacency graph of the surface

Si può vedere un cubo che si rovescia?

Nello spazio euclideo di dimensione n, una riflessione rispetto a un iperpiano non puo` essere realizzata con un movimento rigido. Cio` diventa possibile se si considerano anche movimenti che avvengono nello spazio di dimensione n + 1. In queste note viene illustrato un modo per visualizzare un movimento rigido nello spazio quadridimensionale che realizza una riflessione di un oggetto tridimensionale

The adjacency graph of a real algebraic surface

The paper deals with the question of recognizing the mutual positions of the connected components of a non-singular real projective surface S in the real projective 3-space. We present an algorithm that answers this question through the computation of the adjacency graph of the surface; it also allows to decide whether each connected component is contractible or not. The algorithm, combined with a previous one returning as an output the topology of the surface, computes a set of data invariant up to ambient-homeomorphism which, though not sufficient to determine the pair (RP3; S), give information about the nature of the surface as an embedded object