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We consider the most general AdS$_3$ solutions of type IIB supergravityadmitting a dynamical SU$(3)$ structure and preserving $\mathcal{N}=(0,2)$supersymmetry. The analysis is broken into three distinct classes depending onwhether the dynamical SU$(3)$ structure degenerates to a strict SU$(3)$structure. The first class we consider allows for a holomorphically varyingaxio-dilaton consistent with the presence of $(p,q)$ 7-branes in addition toD3-branes and $(p,q)$ 5-branes. In the remaining two classes the axio-dilatonmay vary but does not do so holomorphically. The second class of solutionallows for 5-branes and 1-branes but no D3-branes, whilst in the final classall branes can be present. We illustrate our results with examples of suchsolutions including a new infinite family with all fluxes but the axion turnedon.

$\mathcal{N}=(0,2)$ AdS$_3$ Solutions of Type IIB and F-theory with Generic Fluxes