  In this paper we discuss algebraic, combinatorial and topological properties
of singular virtual braids. On the algebraic side we state the relations
between classical and virtual singular objects, in addition we discuss a
Birman-like conjecture for the virtual case. On the topological and
combinatorial side, we prove that there is a bijection between singular
abstract braids, horizontal Gauss diagrams and singular virtual braids, in
particular using horizontal Gauss diagrams we obtain a presentation of the
singular pure virtual braid monoid.
