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Summary: THE GEOMETRY OF K3 SURFACES
LECTURES DELIVERED AT THE
SCUOLA MATEMATICA INTERUNIVERSITARIA
CORTONA, ITALY
JULY 31--AUGUST 27, 1988
DAVID R. MORRISON
1. Introduction
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
integer.)
We first try a very straightforward approach to this problem. Let C
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