Rational double points on a normal octicK3 surface

Rational double points on supersingular K3 surfaces

We investigate configurations of rational double points with the total Milnor number 21 on supersingular K3 surfaces. The complete list of possible configurations is given. As an application, we also give the complete list of extremal (quasi-)elliptic fibrations on supersingular K3 surfaces.

Distribution of Rational Points: A Survey

Counting rational points on a certain exponential-algebraic surface

We study the distribution of rational points on a certain exponential-algebraic surface andwe prove, for this surface, a conjecture of A. J. Wilkie. 2000 Mathematics Subject Classification: 11G99, 03C64

The Dynkin Diagrams of Rational Double Points

Rational double points are the simplest surface singularities. In this essay we will be mainly concerned with the geometry of the exceptional set corresponding to the resolution of a rational double point. We will derive the classification of rational double points in terms of Dynkin diagrams.

The Density of Rational Points on Cayley ’ s Cubic Surface

The Cayley cubic surface is given by the equation 4 i=1 X −1 i = 0. We show that the number of non-trivial primitive integer points of size at most B is of exact order B(log B) 6 , as predicted by Manin's conjecture.