| The
classical (topological) Euler characteristic possesses various nice
properties. This allows to use it as a measure in the integration over
the topological spaces/varieties (as introduced by Viro). Then one can
calculate the "Euler volume" of the spaces in different ways,
e.g. by using the classical Fubini theorem. Comparing the answers gives a way to get some classical formulas from topology/enumerative geometry of smooth/singular/reducible plane curves and hypersurfaces. |