Bulk singularities and the effective cosmological constant for higher co-dimension branes

We study a general configuration of parallel branes having co-dimension >2situated inside a compact d-dimensional bulk space within the framework of ascalar and flux field coupled to gravity in D dimensions, such as arises in thebosonic part of some D-dimensional supergravities. A general relation isderived which relates the induced curvature of the observable noncompact ndimensions to the asymptotic behaviour of the bulk fields near the branepositions. For compactifications down to n = D-d dimensions we explicitly solvethe bulk field equations to obtain the near-brane asymptotics, and by so doingrelate the n-dimensional induced curvature to physical near-brane properties.In the special case where the bulk geometry remains nonsingular (or onlyconically singular) at the brane positions our analysis shows that theresulting n dimensions must be flat. As an application of these results wespecialize to n=4 and D=6 and derive a new class of solutions to chiral 6Dsupergravity for which the noncompact 4 dimensions have de Sitter or anti-deSitter geometry