Vector bundles on toric varieties

Moduli of Toric Vector Bundles

We give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as a locally closed subscheme of a product of partial flag varieties cut out by combinatorially specified rank conditions. We use this description to show that...

Principal Parts of Line Bundles on Toric Varieties

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 ...

Toric Vector Bundles and Parliaments of Polytopes

We introduce a collection of convex polytopes associated to a torus-equivariant vector bundle on a smooth complete toric variety. We show that the lattice points in these polytopes correspond to generators for the space of global sections and we relate edges to jets. Using the polytopes, we also exhibit toric vector bundles that are ample but not globally generated, and toric vector bundles tha...

Chern Numbers of Ample Vector Bundles on Toric Surfaces

Let E be an ample rank r bundle on a smooth toric projective surface, S, whose topological Euler characteristic is e(S). In this article, we prove a number of surprisingly strong lower bounds for c1(E) and c2(E). First, we show Corollary (3.2), which says that, given S and E as above, if e(S) ≥ 5, then c1(E) ≥ r2e(S). Though simple, this is much stronger than the known lower bounds over not nec...