We give new examples of algebraic integral cohomology classes on smooth projective complex varieties that are not integral linear combinations of classes of smooth subvarieties. Some of our examples have dimension 6, the lowest possible. The classes that we consider are minimal cohomology classes on Jacobians of very general curves. Our main tool is complex cobordism.

• 14C25 - Algebraic cycles
• 14K12 - Subvarieties of abelian varieties
• 57R77 - Complex cobordism (\(\mathrm{U}\)- and \(\mathrm{SU}\)-cobordism)

• 1 zbMATH Open