Rational points on del Pezzo surfaces of degree 1 and 2
Hassett, Brendan E.
Doctor of Philosophy
One of the fundamental problems in Algebraic Geometry is to study solutions to certain systems of polynomial equations in several variables, or in other words, find rational points on a given variety which is defined by equations. In this paper, we discuss the existence of del Pezzo surface of degree 1 and 2 with a unique rational point over any finite field [Special characters omitted.] , and we will give a lower bound on the number of rational points to each q. Furthermore, we will give explicit equations of del Pezzo surfaces with a unique rational point. Also we will discuss the rationality property of the del Pezzo surfaces especially in lower degrees.
Pure sciences; Del Pezzo surfaces; Algebraic geometry; Mathematics