  We give the necessary and sufficient conditions for warped AdS$_3$ (and
Mink$_3$) solutions of Type II supergravities to preserve ${\cal N}=(2,0)$
supersymmetry, in terms of geometric conditions on their internal space M$_7$.
Such solutions possess a canonical ten-dimensional Killing vector that can be
either time-like or null. In this work we classify the null case in massive
Type IIA supergravity which necessitates that M$_7$ decomposes as a circle
fibration over a six-dimensional base with orthogonal SU(2)-structure
containing a complex four-manifold. We narrow our focus to solutions for which
M$_7$ becomes $\mathbb{T}^2$ fibred over a foliation of a K\"{a}hler manifold
over an interval. We find a class of solutions which are the massive Type IIA
version of GK geometries and present an extremal problem which computes the
central charge of the solution using just topology. Finally, we present
geometric conditions for AdS$_3$ solutions to preserve arbitrary extended
chiral supersymmetry.
