It is probably surprising that algebraic geometry, in particular enumerative
geometry, is very much related to theoretical physics. In fact, many results in enumerative
geometry have been found by physicists first.
In contrast to our previous examples, we have now used a linear projection to map the real
3-dimensional space onto the drawing plane.
We see that there are some lines contained in S. In fact, one can show that every smooth
cubic surface has exactly 27 lines on it. This is another sort of
question that one can ask about the solutions of polynomial equations, and that is not of
topological nature: do they contain curves with special properties (in this case lines), and if
so, how many? This branch of algebraic geometry is usually called enumerative geometry.