We propose a new set of IIB type and eleven-dimensional supergravity
solutions which consists of the n-fold product of two-spaces Hn/Ξ (where Hn denotes the product of n upper half-planes
H2 equipped with the co-compact action of ΞβSL(2,R)n) and (Hn)β/Ξ (where (H2)β=H2βͺ{cuspofΞ} and Ξ is a congruence subgroup of SL(2,R)n). The
Freed-Witten global anomaly condition have been analyzed. We argue that the
torsion part of the cuspidal cohomology involves in the global anomaly
condition. Infinitisimal deformations of generalized complex (and K\"ahler)
structures also has been analyzed and stability theorem in the case of a
discrete subgroup of SL(2,R)n with the compact quotient Hn/Ξ was verified.Comment: 7 pages, no figures. To appear in the Proceedings of XXVIII Workshop
on Geometrical Methods in Physics, Bialowieza (Poland), 28.06 - 04.07.200