  We study BPS jumping loci, or the subloci in moduli spaces of supersymmetric
string vacua where BPS states come into existence discontinuously. This
phenomenon is distinct from wall-crossing. We argue that these loci should be
thought of as special cycles in the sense of Noether-Lefschetz loci or special
Shimura subvarieties, which are indeed examples of BPS jumping loci for certain
string compactifications. We use the Hodge-elliptic genus as an informative
tool, suggesting that our work can be extended to understand the jumping
behavior of motivic Donaldson-Thomas invariants.
