On Higher Syzygies of Projective Toric Varieties

Let A be an ample line bundle on a projective toric variety X of dimension n (&#8805; 2). It is known that the d-th tensor power A&#8855;d embedds X as a projectively normal variety in Pr := P(H0(X,L&#8855;d)) if d &#8805; n &#8722; 1. In this paper first we show that when dimX = 2 the line bundle A&#8855;d satisfies the property Np for p &#8804; 3d &#8722; 3. Second we show that when dimX = n &#8805; 3 the bundle A&#8855;d satisfies the property Np for p &#8804; d &#8722; n + 2 and d &#8805; n &#8722; 1.</p

A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I

We introduce a class of gapped Hamiltonians on quantum spin chains, which allows asymmetric edge ground states. This class is an asymmetric generalization of the class of Hamiltonians in [FNS]. It can be characterized by five qualitative physical properties of ground state structures. In this Part I, we introduce the models and investigate their properties.Comment: Final versio

Ample line bundles on a certain toric fibered 3-folds

Let $X$ be a projective nonsingular toric 3-fold with a surjective torus equivariant morphism onto the projective line. Then we prove that an ample line bundle on $X$ is always normally generated.Comment: 12 pages, 3 figure