On partially ample divisors

Partially ample divisors are defined by relaxing the different conditions that characterize the ample divisors. We prove that for nef and big divisors such notions coincide. We also prove that the partial ampleness of big divisors are preserved in the positive parts of the Fujita‐Zariski decomposition.     

On partially ample adjoint divisors

We study the MMP (minimal model program) invariant properties of partially ample adjoint divisors. Using these invariant properties, we prove that the three notions of (numerically, cohomologically, asymptotically) partial ampleness coincide for big divisors on Q$\mathbb{Q}$-factorial Fano type varieties and more generally Mori dream spaces. This gives a partial answer to a question raised by Totaro.     

Characterizing projective bundles by means of ample divisors

Let X be a complex projective manifold and AX a non-singular hypersurface which is an ample divisor having characteristic cycles A_i non-singular in every dimension i0. The pairs (X,A) such that g(A₁)=h^1,0 (X) are characterized.     

Classification of polarized manifolds admitting homogeneous varieties as ample divisors

We give a complete classification of smooth polarized varieties (X, L) such that the linear system |L| has a homogeneous member A.     

On stable and ample vector bundles of rank 2 on curves

Ohne Zusammenfassung     

On divisors of a quadratic form

An approximation is given for the number of divisors of the quadratic formn²+m²+t².Supported by University of the Basque Country.     

An example of a polarized K3 surface with elliptic free Clifford divisors

Let (S, L) be a polarized K3 surface consisting of a Kummer surface S constructed from a product abelian surface of two elliptic curves which are not mutually isogenous and a base point free line bundle L such that L ² > 0. In this paper, we give some sufficient conditions for the existence of elliptic free Clifford divisors on (S, L).     

On a class of divisors of matrices

We propose a structural criterion for divisibility of matrices over a commutative principal ideal domain. Under certain restrictions we exhibit a method of finding all the non-associate divisors that have a prescribed canonical diagonal form.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 13–19.     

On the varieties of special divisors

Based on a relation between the varieties W_d^r(C) of special divisors on a curve C and subloci of effective divisors on C imposing a suitable number of conditions on a certain linear series we develop a tool for the construction of irreducible components of W_d^r(C). Using this we discover new irreducible components of W_d^r(C), for a general k-gonal curve C of genus g, and in some cases we can identify the duals of these components in K_C − W_d^r(C) = W_d′^r′(C)(d′ = 2g − 2 − d, r′ = g − 1 − d + r).