Nontrivial Massey products on compact Kähler manifolds
Giovanni Placini, Jonas Stelzig, Leopold ZollerAbstract
By a result of Deligne, Griffiths, Morgan, and Sullivan, compact Kähler manifolds are rationally formal. In contrast to this, we show that the pluripotential quasi‐isomorphism type of the bigraded, bidifferential algebra of forms on a compact Kähler manifold generally contains more information than the de Rham cohomology algebra with its real Hodge structure. More precisely, on any compact Kähler manifold fibering over a Riemann surface of genus at least two, there is a nontrivial ‐Massey product. Furthermore, starting from dimension three, there are simply connected projective manifolds with a nonzero ‐Massey product of three divisor classes. In particular, compact Kähler manifolds are generally not formal in the sense of pluripotential homotopy theory.