In this paper, we give a geometric proof of Pinkham's theorem on the positive cycles supported on the exceptional divisor of a rational singularity. In order to do this, we give several properties of the Tyurina components of the exceptional divisor and of the points of blowing-up surface of a rational singularity.
TOSUN, MERAL (1999) "Tyurina Components and Rational Cycles for Rational Singularities," Turkish Journal of Mathematics: Vol. 23: No. 3, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol23/iss3/2