Signed Mukai diagonals and derived equivalences of fivefolds
For every Hochschild diagonal of a smooth projective complex variety, a Fourier–Mukai equivalence preserves both the ordinary Hodge-number sum and the sum signed by the parity of the antiholomorphic degree. The latter is the signature of a Hermitian form obtained from the generalized Mukai pairing. In dimension five these invariants determine $h^{0,3}$ and $h^{1,4}$ and reduce the unrestricted Hodge-number problem to two numerical parameters, one of which is the possible failure of invariance of $h^{0,2}$. Albanese methods remove this structure-sheaf ambiguity when the Albanese image has…
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