Toric co-Higgs bundles on toric varieties

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 ...

Minicourse on Toric Varieties

1. Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Characters and 1-Parameter Subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3. Toric Varieties . . . . . . . . . . . . . . . . . . . . . . . . . ....

Lectures on Toric Varieties

1 Four constructions 1 1.1 First construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Second construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Third construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourth construction . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Comments on toric varieties

Here are few notes on not necessarily normal toric varieties and resolution by toric blow-up. These notes are independent of, but in the same spirit as the earlier preprint [Tho03]. That is, they focus on the fact that toric varieties are locally given by monoid algebras. 1 Not necessarily normal toric varieties Fix a base field k. We start by recalling the definition of a fan. Let N ∼= Z be a ...