Moduli spaces of coherent sheaves on multiple curves

Jean-Marc Drézet (1)

1 IMJ - Institut de Mathématiques de Jussieu

In this paper we study coherent sheaves on reduced curves that can be locally embedded in smooth surfaces. We define new invariants for these sheaves : the generalized rank and degree, and prove a Riemann-Roch theorem using them. The quasi locally free sheaves are natural generalizations of locally free ones. We describe some moduli spaces of stable such sheaves on double curves.

Mots clés: primitive multiple curves; coherent sheaves

Domaines: Géométrie algébrique [math.AG]

Jean-Marc Drézet. Moduli spaces of coherent sheaves on multiple curves. Piotr Pragacz. Algebraic cycles, sheaves, shtukas, and moduli; Impanga lecture notes, Birkhäuser, pp.33-44, 2008, Trends in Mathematics, 978-3-7643-8536-1. ⟨hal-00742512⟩