Raynaud vector bundles

Abstract

We construct vector bundles R rk µ on a smooth projective curve X having the property that for all sheaves E of slope µ and rank rk on X we have an equivalence: E is a semistable vector bundle ⇐⇒ Hom(R rk µ , E) = 0. As a byproduct of our construction we obtain effective bounds on r such that the linear system |R · Θ| has base points on U X (r, r(g − 1)).⊗rR(g−1)−dR 1 . This implies that F itself is a semistable bundle of slope 2.1 Construction of S µ,R,m for µ ∈ [−g − 1, −g)

Some examples of vector bundles in the base locus of the generalized theta divisor

“…Some improvements on those results were obtained in [1,4]. Finally, [5] gave, at least theoretically, a characterization of all the points in the base locus (see also [6]). In sharp contrast with the degree zero case, not much has been done for other degrees, the main reason being that a characterization of fixed points was not available till the Strange Duality Conjecture was proved in [7] (see also [2]).…”

Postnikov-Stability for Complexes on Curves and Surfaces

“…The specications for the construction are given in the proof below. For more details on F r,d and its properties see the article [9] (ii') There exists a vector bundle…”

Parabolic Raynaud bundles

“…We can compute the rank and degree of R r,d in terms of the genus g Y of Y and the integers r and d (see Proposition 2.2 and Corollary 3.4 in [6]). …”

“…In [6], building on Popa's result it was shown that Raynaud bundles exist. In [3], an analog of Faltings' semistability criterion is given for parabolic vector bundles.…”