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A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line

4 votes

difference of curve classes

Yes, this is possible. For an example of a Calabi-Yau threefold with such differences of curves, see my paper with Pavanelli http://arxiv.org/pdf/math/0512182.pdf. I am sure there are much simpler exa …
Mark Gross's user avatar