A cubic surface is defined to be a surface that is defined as a vanishing set of cubic polynomials. In 1849, Cayley and Salmon showed that there are exactly 27 lines on a smooth cubic surface. Through the introduction of new tools in algebraic geometry in the 20th century, a more streamlined proof has been made. Namely, by introducing linear systems and blow-ups, this talk will showcase how we can get these 27 lines.
Linear Systems, Blow-ups, and Cubic Surfaces