Spanned vector bundles with canonical determinant on special curves
Received: 19 February 2009
Accepted: 9 March 2009
Mathematics Subject Classification (2000): 14H60 - 14H40 - 14C25 - 14M15
Keywords: Spanned vector bundle; canonical determinant; higher cycle map; Jacobian; Griffiths group.
The author was partially supported by MIUR and GNSAGA of INdAM (Italy).
Abstract Let C be a smooth curve of genus g. Here we construct (under geometric restrictions, like C hyperelliptic or a complete intersection) spanned rank n vector bundles E on C with canonical determinant and with a (2n+1)-dimensional linear subspace W ⊆ H0(E) such that the natural wedge map Λn(W) → H0(det(E)) is injective. The motivation came from a paper by Pirola and Rizzi, who used (E,W) to get certain non-trivial higher cycle maps on the relative jacobian of an n-dimensional family of curves C → S with C as a fiber.