Related papers: The map defined by a non-very ample line bundle on…

We prove some results on effective very ampleness and projective normality for some varieties with trivial canonical bundle. In the first part we prove an effective projective normality result for an ample line bundle on regular smooth…

We prove that any smooth complex projective variety with generic vanishing index bigger or equal than 2 has birational bicanonical map. Therefore, if X is a smooth complex projective variety X with maximal Albanese dimension and…

This paper provides some technical results needed in "Formalism for Relative Gromov-Witten Invariants." We study line-bundles on the moduli stacks of relative stable and rubber maps that are used to define relative Gromov-Witten invariants…

The main purpose of this paper is to prove the following theorem on the defect relations for ample divisors of abelian varieties. Main Theorem. Let $A$ be an abelian variety of complex dimension $n$ and $D$ be an ample divisor in $A$. Let…

In this paper, we prove abundance for non-uniruled 3-folds with non-trivial Albanese maps, over an algebraically closed field of characteristic $p > 5$. As an application we get a characterization of abelian 3-folds.

Let $(S,L_{S})$ be a polarized abelian surface, and let $M = c \cdot \pi^*L_S - \alpha \cdot \sum_{i=1}^r E_i$ be a line bundle on ${\rm Bl}_{r}(S)$, where $\pi:{\rm Bl}_{r}(S) \rightarrow S$ is the blow-up of $S$ at $r$ general points with…

We completely describe the Brill-Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers $d$ and $r$, consider the variety $V^r_d(|H|)$ parametrizing curves $C$ in the…

We start the classification of smooth projective threefolds X whose anticanonical bundles -K_X are big and nef but not ample. In this paper we treat the case b_2(X) = 2 and the morphism associated with the base point free linear system…

Let $\pi\,:\, X \,\longrightarrow\, Y$ be a finite morphism of smooth projective varieties defined over an algebraically closed field of characteristic zero. We study the necessary and sufficient criteria for $\pi$ such that there exists a…

We study the birationality (onto its image) of the Abel-Prym morphism associated with a Prym-Tuyrin variety. We use such result to prove that Picard bundles over Prym varieties are simple and moreover they are stable when the Abel-Prym…

The purpose of this note is to show that $2K$ of any smooth compact complex two ball quotient is very ample, except possibly for four pairs of fake projective planes of minimal type, where $K$ is the canonical line bundle. For the four…

The families of morphisms of vector fibre bundle (\cite{Mill1}) defined by the linear Hamiltonian systems of differential equations is considered. Authors proved that the specified families of morphisms is not saturated (\cite{Mill2}).

We show that the vector bundle associated to a smooth projective connected finite covering of a simple complex abelian variety is ample (under a simple necessary condition). This result is obtained by showing that this bundle is M-regular…

Very ampleness criteria for rank 2 vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.

In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system $|L|$ of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after…

We study ample stable vector bundles on minimal rational surfaces. We give a complete classification of those moduli spaces for which the general stable bundle is both ample and globally generated. We also prove that if $V$ is any stable…

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.

We use constructions of surfaces as abelian covers to write down exceptional collections of line bundles of maximal length for every surface $X$ in certain families of surfaces of general type with $p_g=0$ and $K_X^2=3,4,5,6,8$. We also…

In this paper, we study rational sections of the relative Picard variety of a linear system on a smooth projective variety. Specifically, we prove that if the linear system is basepoint-free and the locus of non-integral divisors has…

Let $X$ be a projective manifold of dimension $n$ and $L$ a strictly nef line bundle on $X$. Then $K_X+tL$ is ample if $t > n+1$ in the following cases. 1.) $\text{dim} X = 3$ unless (possibly) $X$ is a Calabi-Yau with $c_2 \cdot L=0$; 2.)…