2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64830The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results are proved, having moduli theoretic applications. In particular, certain strata of the moduli space of stable curves are characterized by a (finite) set of integers, measuring the non-reducedness of the scheme of spin curves, and definable in purely graph-theoretical terms.LaTeX, 16 pages, 30 figuresAlgebraic GeometryCombinatorics14H10, 05C75text