Summary: THE GEOMETRY OF K3 SURFACES LECTURES DELIVERED AT THE
SCUOLA MATEMATICA INTERUNIVERSITARIA JULY 31--AUGUST 27, 1988
DAVID R. MORRISON This is a course about K3 surfaces and several
related topics. I want to begin by working through an example
which will illustrate some of the techniques and results we will
encounter during the course. So consider the following problem.
Problem . Find an example of C X P3 , where C is a smooth curve
of genus 3 and degree 8 and X is a smooth surface of degree 4.
Of course, smooth surfaces of degree 4 are one type of K3
surface. (For those who don't know, a K3 surface is a (smooth)
surface X which is simply connected and has trivial canonical
bundle. Such surfaces satisfy (OX ) = , and for every divisor D
on X, D · D is an even We first try a very straightforward
approach to this problem. Let C