Espaces de modules de systèmes cohérents, I: normalité

Abstract

Given a polynomial α > 0 with rational coefficients, we define the notion of αsemistable coherent system on projective algebraic manifolds. We prove that the moduli spaces of coherent systems over P 2 (C) which appear in the study of Donaldson numbers of the projective plane are irreducible and normal, once the Hilbert polynomial and the order of the coherent system are fixed.