Matthias Paulsen (Hannover) - Unirational counterexamples to the IHC of torsion type
Counterexamples to the integral Hodge conjecture can arise either from torsion cohomology classes (as in Atiyah's and Hirzebruch's original counterexample from 1961) or from non-torsion classes (as first seen in Kollár's counterexample from 1991). After Voisin proved the IHC for uniruled threefolds, Schreieder found a unirational fourfold where the IHC fails. His construction of a non-algebraic Hodge class relies on abstract arguments with unramified cohomology. It was an open question whether this class is of torsion type. In this talk, I want to explain a new method that gives an explicit geometric description of the unramified cohomology class appearing in his argument. In particular, this approach allows to prove that Schreieder's unirational counterexample is of torsion type.
Published Sep. 13, 2022 12:37 PM - Last modified Nov. 16, 2022 8:59 PM