  This article is devoted to studying complex algebraic sets under (global)
blow-spherical equivalence. The main results of this article are complete
classifications of complex algebraic curves. Firstly, we present a complete
classification of complex algebraic curves under blow-spherical homeomorphisms
at infinity and, then, we present a complete classification of complex
algebraic curves under (global) blow-spherical homeomorphisms. We also present
several properties of the blow-spherical equivalence. For instance, we prove
that the degree of curves is preserved under blow-spherical homeomorphisms at
infinity. Another property presented here is a Bernstein-type result which says
that a pure dimensional complex algebraic set which is blow-spherical
homeomorphic at infinity to a Euclidean space must be an affine linear
subspace.
