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We study BPS jumping loci, or the subloci in moduli spaces of supersymmetricstring vacua where BPS states come into existence discontinuously. Thisphenomenon is distinct from wall-crossing. We argue that these loci should bethought of as special cycles in the sense of Noether-Lefschetz loci or specialShimura subvarieties, which are indeed examples of BPS jumping loci for certainstring compactifications. We use the Hodge-elliptic genus as an informativetool, suggesting that our work can be extended to understand the jumpingbehavior of motivic Donaldson-Thomas invariants.

BPS jumping loci and special cycles