at the field equation(s) for the antisymmetric tensor field(s).

Standard intersections
----------------------

There are three single $p$-branes with a near-horizon geometry $adS_{p+2} \xx S^{D-p-2}$: the $M2$, $M5$ and $D3$ branes. We now recall the solutions based on the standard intersections and show that they are related by a simple rule which we will call the wave/monopole rule.

   (a)           $M2\perp M5$           $adS_3\times E^5\times S^3$
  ----- ------------------------------ ------------------------------
   (b)       $M2\perp M2\perp M2$       $adS_2\times E^6\times S^3$
   (c)       $M5\perp M5\perp M5$       $adS_3\times E^6\times S^2$
   (d)   $M2\perp M2\perp M5\perp M5$   $adS_2\times E^7 \times S^2$

  : [*Standard intersection of M branes with anti-de Sitter near-horizon geometries.*]{}

Table 2 shows the intersections and their near-horizon geometries [@KK; @BPS1]. In [@BPS1] it was further demonstrated that the near-horizon limits of these intersections exhibit supersymmetry doubling. Thus, $M2\perp M5$ preserves $1/4$ and its near-horizon limit $1/2$ of supersymmetry. The other three intersections have supersymmetry enhancement from $1/8$ to $1/4$.

Roughly speaking, the wave/monopole rule asserts that starting from the solution with near-horizon geometry containing $adS_3$ and $S^3$ factors (the $M2\perp M5$ intersection in table 2), one can get all the others simply by adding a wave and/or monopoles. A wave effectively replaces $adS_3$ by $adS_2$ and a monopole $S^3$ 