NORMAL GENERATION OF NONSPECIAL LINE BUNDLES ON ALGEBRAIC CURVES

Normal generation of very ample line bundles on toric varieties ∗

Let A and B be very ample line bundles on a projective toric variety. Then, it is proved that the multiplication map Γ(A)⊗ Γ(B) → Γ(A⊗B) of global sections of the two bundles is surjective. As a consequence, it is showed that any very ample line bundle on a projective toric variety is normally generated. As an application we show that any ample line bundle on a toric Calabi-Yau hypersurface is ...

Normal generation of line bundles on multiple coverings

Any line bundle L on a smooth curve C of genus g with degL ≥ 2g+1 is normally generated, i.e., φL(C) ⊆ PH(C,L) is projectively normal. However, it has known that more various line bundles of degree d failing to be normally generated appear on multiple coverings of genus g as d becomes smaller than 2g+1. Thus, investigating the normal generation of line bundles on multiple coverings can be an ef...

Vector bundles over algebraic curves

Line Bundles and Curves on a

Orders on surfaces provided a rich source of examples of noncommutative surfaces. In [HS05] the authors prove the existence of the analogue of the Picard scheme for orders and in [CK11] the Picard scheme is explicitly computed for an order on P ramified on a smooth quartic. In this paper, we continue this line of work, by studying the Picard and Hilbert schemes for an order on P ramified on a u...

Exact sequences of semistable vector bundles on algebraic curves

Let X be a smooth complex projective curve of genus g ≥ 1. If g ≥ 2, assume further that X is either bielliptic or with general moduli. Fix integers r, s, a, b with r > 1, s > 1 and as ≤ br. Here we prove the existence of an exact sequence 0 → H → E → Q → 0 of semistable vector bundles onX with rk(H) = r, rk(Q) = s, deg(H) = a and deg(Q) = b.