5, we present a study of the supersymmetry near the horizon of $D$-brane solutions in arbitrary frames. We find that the dual $Dp$-frame, i.e. the frame in which the curvature and the $(8{-}p)$-form field strength appear in the action with the same power of the dilaton, represents a “threshold” frame for supersymmetry enhancement. In addition, in this frame the near-horizon geometry factorizes into the product $adS_{p+2} \xx S^{8-p}$ for $p\neq 5$, whereas for $p=5$ it becomes ${\cal M}_7 \xx S^3$. In section 6, we use the new solutions to obtain several results about new vacua of gauged supergravities. We also point out the possibility of a new gauged supergravity in $5d$. Section 7 contains our conclusions. Finally, in the Appendix we present a Kaluza-Klein ansatz inspired by the new solutions and we explicitly compute the Killing spinors of the $adS_2 \xx S^2 \xx S^2 \xx E^5$ solution.

Intersections with anti-de Sitter near-horizon limits
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In this section we describe special supersymmetric intersections of branes which in their near-horizon limit have a factorized geometry involving an anti-de Sitter spacetime and some other (compact) manifolds. Most of them are found as solutions to $D=11$ supergravity but in some cases we have to 