2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/211047We study the spectral geometry of the quantum projective plane CP^2_q, a deformation of the complex projective plane CP^2, the simplest example of a spin^c manifold which is not spin. In particular, we construct a Dirac operator D which gives a 0^+ summable spectral triple, equivariant under U_q(su(3)). The square of D is a central element for which left and right actions on spinors coincide, a fact that is exploited to compute explicitly its spectrum.v2: 26 pages. Paper completely reorganized; no major change, several minor onesQuantum AlgebraHigh Energy Physics - TheoryMathematical Physics58B34, 17B37text