About: Virtual fundamental class

In mathematics, specifically enumerative geometry, the virtual fundamental class of a space is a replacement of the classical fundamental class in its chow ring which has better behavior with respect to the enumerative problems being considered. In this way, there exists a cycle with can be used for answering specific enumerative problems, such as the number of degree rational curves on a quintic threefold. For example, in Gromov–Witten theory, the for the class of a line in . The non-compact "smooth" component is empty, but the boundary contains maps of curves