This is the text of the poster you can see here.

The devil’s mischief

“Fifty years ago we used to say that if algebraic curves were God’s creation, then algebraic surfaces were the Devil’s mischief”.
With this sentence, Federigo Enriques gave an account in 1949 (in his work Algebraic surfaces) of the difficult problem that he had solved in 1914 together with Guido Castelnuovo: the classification (with respect to birational transformations) of algebraic surfaces, i.e., of surfaces which can be described via polynomial equations, like those depicted in this poster.
The images in this poster are the photographs of some plaster models of algebraic surfaces belonging to the Math Department “F. Enriques”, Università degli Studi di Milano. Clearly, the plaster model is a three-dimensional object. It is the “skin” that gives us the idea of a surface, which sometimes should be imagined unbounded.
Techniques and concepts applied to curves can not be tout court generalized to the investigation of surfaces. On the one hand, this explains Enriques’ sentence; on the other hand, it shows that analogy is not enough although it is an important instrument for a researcher.

The models in the photos above here are examples of surfaces given by degree two polynomials or, briefly, degree two surfaces (quadrics). Those of the photos below here are examples of degree three surfaces (cubics), and those of the leaflet Algebraic surfaces II are examples of degree four surfaces (quartics).

As you can see, two quadrics can already be very different: some of them are bounded (i.e., like the11269, the so called ellipsoid, are contained in a bounded region of three space), while others, like the 11268 or the 11295 are not; some of them are “made up by just one piece”, while others, like the11265 are not; Some of them are ruled, like the 11273 and the 11276 (and models like the 11349 and the 11295 show better this property) while others are not. Some of them are “smooth”, while others have singularities as the vertex of the yellow cone which you see in the 11349 together with the other smooth surface.