Hi there,

I want to ask about the 2-cycle of K3 surface.

As we know, its betti number $b_2$=22, so there will be 22 2-cycle generators.

Is there any topological way to figure out such cycles direct?

For example, in the best case, if the K3 surface is elliptic and has a global section, can we use combinations of fibre and section to represent all the 22 2-cycles?

Thanks!