In this paper, we classify smooth toric Fano 5-folds of index 2. There exist exactly 10 smooth toric Fano 5-folds of index 2 up to isomorphisms.

In this paper, we classify projective toric birational morphisms from Gorenstein toric 3-folds onto the 3-dimensional affine space with relatively ample anti-canonical divisors.

We introduce and study the toric Hilbert scheme that parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal.

We present a self-contained combinatorial approach to Fujita’s conjectures in the toric case. Our main new result is a generalization of Fujita’s very ampleness conjecture for toric varieties with arbitrary singularities. In an appendix, we use similar methods to give a new proof of an anologous toric generalization of Fujita’s freeness conjecture due to Fujino. Given an ample divisor D and any...

Starting from the data of a nonsingular complex projective toric variety, we define an associated notion co-Higgs bundle. We provide Lie-theoretic classification these objects by studying interaction between Klyachko's fan filtration and fiber bundle at closed point in open orbit torus action. This can be interpreted, under certain conditions, as construction coarse moduli scheme bundles any ra...

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 ...

In this article, we determine the explicit toric variety structure of Hilb1(Cn) for n = 4, 5, where A1(n) is the special diagonal group of all order 2 elements. Through the toric data of Hilb1(Cn), we obtain certain toric crepant resolutions of C/A1(n), and the different crepant resolutions are connected by flops of n-folds for n = 4, 5. 2000 MSC: 14M25,14J17, 20C33