  As a continuation of our previous work (arXiv:0708.4333) an algebraic
geometrical study of a single $d$-dimensional qudit is made, with $d$ being
{\it any} positive integer. The study is based on an intricate relation between
the symplectic module of the generalized Pauli group of the qudit and the fine
structure of the projective line over the (modular) ring $\bZ_{d}$. Explicit
formulae are given for both the number of generalized Pauli operators commuting
with a given one and the number of points of the projective line containing the
corresponding vector of $\bZ^{2}_{d}$. We find, remarkably, that a perp-set is
not a set-theoretic union of the corresponding points of the associated
projective line unless $d$ is a product of distinct primes. The operators are
also seen to be structured into disjoint `layers' according to the degree of
their representing vectors. A brief comparison with some multiple-qudit cases
is made.
