2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196263We study massless deformations of generalized calibrated cycles, which describe, in the language of generalized complex geometry, supersymmetric D-branes in N=1 supersymmetric compactifications with fluxes. We find that the deformations are classified by the first cohomology group of a Lie algebroid canonically associated to the generalized calibrated cycle, seen as a generalized complex submanifold with respect to the integrable generalized complex structure of the bulk. We provide examples in the SU(3) structure case and in a `genuine' generalized complex structure case. We discuss cases of lifting of massless modes due to world-volume fluxes, background fluxes and a generalized complex structure that changes type.52 pages, added references, added comment on ellipticity in appendix B, made minor changes according to instructions referee JHEPHigh Energy Physics - TheoryDifferential Geometrytext