Related papers: Elliptic surfaces and linear systems with fat poin…

We prove that any number of general fat points of any multiplicities impose the expected number of conditions on a linear system on a smooth projective surface, in several cases including primitive linear systems on very general K3 and…

Atiyah classifies vector bundles on elliptic curves $E$ over an algebraically closed field of any characteristic. On the other hand, a rank $2$ vector bundle on $E$ defines a surface $S$ with a $\mathbb{P}^1$-bundle structure on $E$. We…

In this note we relate about the problem of evaluate the dimension of linear systems through fat points defined on generic $K3$ surfaces.

Let X be a smooth projective surface. Here we study the postulation of a general union Z of fat points of X, when most of the connected components of Z have multiplicity 2. This problem is related to the existence of "good" families of…

In the paper we develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne Conjecture holds for systems with base points of equal…

We study deformation theory of elliptic fibre bundles over curves in positive characteristics. As applications, we give examples of non-liftable elliptic surfaces in charactertic two and three, which answers a question of Katsura and Ueno.…

We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an…

In this paper we introduce a technique to degenerate K3 surfaces and linear systems through fat points in general position on K3 surfaces. Using this degeneration we show that on generic K3 surfaces it is enough to prove that linear systems…

We translate the Atiyah's results on classification of vector bundles on elliptic curves to the language of factors of automorphy.

We proved that the general members of Severi varieties on an Atiyah ruled surface over a general elliptic curve have nodes and ordinary triple points as singularities.

We give a classification of the log canonical models of elliptic surface pairs consisting of an elliptic fibration, a section, and a weighted sum of marked fibers. In particular, we show how the log canonical models depend on the choice of…

A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven…

Given a minimal surface equipped with a generically finite map to an Abelian variety, we give an optimal bound on the canonical degree of a rational or an elliptic curve. As a corollary, we obtain the finiteness of rational and elliptic…

Let S be a smooth algebraic surface satisfying the following property: H^i(\oc_S(C))=0 (i=1,2) for any irreducible and reduced curve C of S. The aim of this paper is to provide a characterization of special linear systems on S which are…

We consider K3 surfaces which are double cover of rational elliptic surfaces. The former are endowed with a natural elliptic fibration, which is induced by the latter. There are also other elliptic fibrations on such K3 surfaces, which are…

We consider the open problem of determining the graded Betti numbers for fat point subschemes supported at general points of the projective plane. We relate this problem to the open geometric problem of determining the splitting type of the…

We study the connection between the generation of a fat point scheme supported at general points in the plane and the behaviour of the cotangent bundle with respect to some rational curves particularly relevant for the scheme. We put…

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…

We study linear systems of surfaces in $\mathbb{P}^3$ singular along general lines. Our purpose is to identify and classify special systems of such surfaces, i.e., those nonempty systems where the conditions imposed by the multiple lines…

We explore Bott Vanishing for elliptic surfaces over $\mathbb{P}^1$. We show that Bott Vanishing is singnificantly affected by the geometric properties that whether there exists certain type of singular fibers on the elliptic fibration such…