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We obtain the complete local solutions with 16 supersymmetries to Type IIBsupergravity on a space-time of the form $AdS_{2}\times S^{6}$ warped over aRiemann surface $\Sigma$ in terms of two locally holmorphic functions on$\Sigma$. We construct the general Ansatz for the bosonic supergravity fieldsand supersymmetry generators compatible with the $SO(2,1)\oplus SO(7)$ isometryalgebra of space-time, which extends to the corresponding real form of theexceptional Lie superalgebra $F(4)$. We reduce the BPS equations to thisAnsatz, obtain their general local solutions, and show that these localsolutions solve the full Type IIB supergravity field equations and Bianchiidentities. We contrast the $AdS_{2}\times S^{6}$ solution with the closelyrelated $AdS_6\times S^2$ case and present our results for both in parallel.Finally, we present a preliminary analysis of positivity and regularityconditions for $AdS_{2}\times S^{6}$, but postpone the construction of globallyregular solutions to a subsequent paper.

$AdS_2 \times S^6$ versus $AdS_6 \times S^2$ in Type IIB supergravity