2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150191We make precise the structure of the first two reduction morphisms associated with codimension two nonsingular subvarieties of quadrics $\Q{n}$, $n\geq 5$. We give a coarse classification of the same class of subvarieties when they are assumed to be not of log-general-type. Keywords: Adjunction Theory, classification, codimension two, conic bundles, low codimension, non log-general-type, quadric, reduction, special varietyLatex; 16 pagesAlgebraic Geometry14C05, 14E05, 14E25, 14E30, 14E35, 14J10, 14J30, 14J35, 14J40, 14J45, 14M07text