{"id":"hexagon/2609.00147","pdf":"https://hexagonmath.org/pdf/2609.00147v1","url":"https://hexagonmath.org/abs/2609.00147v1","tags":["msc:14F08","Derived categories","fivefolds"],"score":0,"title":"Signed Mukai diagonals and derived equivalences of fivefolds","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Benjamin Antieau"],"reviews":0,"subject":"math.AG","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-09-30","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}