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We extend our previous construction of global solutions to Type IIB supergravity that are invariant under the superalgebra $F(4)$ and are realized on a spacetime of the form $AdS_6 \times S^2$ warped over a Riemann surface $\Sigma$ by allowing the supergravity fields to have non-trivial $SL(2,{\mathbb R})$ monodromy at isolated punctures on $\Sigma$.
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