\xx S^3$ (b)]{}]{} (4,3)[(4,1)[$adS_3 \xx S^2$ (c)]{}]{} (6,4)[(0,1)[2]{}]{} (2,4)[(2,1)[4]{}]{} (4,6)[(4,1)[$adS_3 \xx S^3$ (a)]{}]{} (1.5,2)[$M$]{} (6.2,5)[$M$]{} (4,1.7)[$W$]{} (4,4.7)[$W$]{} (7.5,7.5)[(4,1)[$\#$ charges]{}]{} (7.5,6)[(4,1)[$2$]{}]{} (7.5,3)[(4,1)[$3$]{}]{} (7.5,0)[(4,1)[$4$]{}]{}

Non-standard intersections
--------------------------

We now turn to intersections with near-horizon geometries of the form $adS_k \xx S^l \xx S^m \xx E^n$ with $k,l,m$ equal to 2 or 3. As we will see, all such configurations involve at least one pair of branes intersecting in the non-standard way, and therefore the harmonic functions will depend on relative transverse coordinates. It was shown in [@CT] that the near-horizon limit of the intersection of two ten-dimensional NS five-branes over a line[^8] has geometry ${\cal M}_4 \xx S^3 \xx S^3$, covariantly constant field strength and a linear dilaton. Addition of a fundamental string along the common direction of the five-branes yields a solution with near-horizon geometry $adS_3 \xx S^3 \xx S^3 \xx E^1$ and constant dilaton, provided the harmonic function of the string is the product of the five-brane harmonic functions [@CT]. In $D=11$ the analogous solution is the intersection of two $M5$ branes over a line, plus a membrane: $$\begin{array}{lccccccccccc}
M5_1 & 1 &   & 3 & 4 & 5 & 6 &   &   &   &    & \\
M5_2 & 1 