The number of 1-codimensional cycles on projective varieties

Abstract

In this article, we investigate the converging radius of the “generalized zeta function,” which is, roughly speaking, the generating function of the number of effective cycles. In Section 3, we give the explicit value of the converging radius when the codimension of the cycles is $1$. In Section 4, we deal with $1$-dimensional cycles on a projective space and give a lower bound of the convergent radius.