Seminar des SFB/TRR 326 GAUSTorsion in Griffiths Groups

The Griffiths group Griff^i(X) of a smooth complex projective variety X is the group of nullhomologous codimension−i cycles on X modulo algebraic equivalence. Recently Schreieder gave the first examples of smooth complex projective varieties X for which the Griffiths group has infinite torsion. In his examples the infinitely many torsion classes are of order 2. In this talk we show that for any integer n ≥ 2, there is a smooth complex projective 5−fold X whose third Griffiths group contains infinitely many torsion elements of order n.