2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65958The zeta-function of a complex variety is a power series whose nth coefficient is the nth symmetric power of the variety, viewed as an element in the Grothendieck ring of complex varieties. We prove that the zeta-function of a surface is rational if and only if its Kodaira dimension is negative.26 pagesAlgebraic Geometry14E99; 14G10text