We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classes. The proof uses the definability of period mappings in the o-minimal structure $\mathbb{R}_{\mathrm{an},\exp}$.

• 03C64 - Model theory of ordered structures; o-minimality
• 14C30 - Transcendental methods, Hodge theory (algebro-geometric aspects)
• 14D07 - Variation of Hodge structures (algebro-geometric aspects)
• 22F30 - Homogeneous spaces