2604.01181 The Betti Number Rigidity Phenomenon: Smooth Fano Varieties of Fixed Dimension and Index Have at Most 3 Distinct Betti Number Profiles
We establish a rigidity phenomenon for the Betti numbers of smooth Fano varieties: for any fixed pair (d, r) of dimension d and Fano index r, the number of distinct Betti number profiles beta(X) = (b_0, b_2, b_4, ..., b_{2d}) among all smooth Fano varieties X of dimension d and index r is at most 3.