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As a continuation of our previous work (arXiv:0708.4333) an algebraicgeometrical study of a single $d$-dimensional qudit is made, with $d$ being{\it any} positive integer. The study is based on an intricate relation betweenthe symplectic module of the generalized Pauli group of the qudit and the finestructure of the projective line over the (modular) ring $\bZ_{d}$. Explicitformulae are given for both the number of generalized Pauli operators commutingwith a given one and the number of points of the projective line containing thecorresponding vector of $\bZ^{2}_{d}$. We find, remarkably, that a perp-set isnot a set-theoretic union of the corresponding points of the associatedprojective line unless $d$ is a product of distinct primes. The operators arealso seen to be structured into disjoint `layers' according to the degree oftheir representing vectors. A brief comparison with some multiple-qudit casesis made.

Projective Ring Line of an Arbitrary Single Qudit