Related papers: ACM bundles on del Pezzo surfaces

We classify indecomposable aCM bundles of rank $2$ on the del Pezzo threefold of degree $7$ and analyze the corresponding moduli spaces.

Some classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank-2 ample vector bundles with $c_2$ less than 7 on Hirzebruch surfaces, and with…

It is well-known that del Pezzo surfaces of degree $9-n$ one-to-one correspond to flat $E_n$ bundles over an elliptic curve. In this paper, we construct $ADE$ bundles over a broader class of rational surfaces which we call $ADE$ surfaces,…

Let $X \subset \mathbb P^3$ be a smooth hypersurface of degree $6$ over complex numbers. In this paper, we give a characterization of initialized and ACM bundles of rank $1$ on $X$ with respect to the line bundle given by a smooth…

A minimal family of curves on an embedded surface is defined as a 1-dimensional family of rational curves of minimal degree, which cover the surface. We classify such minimal families using constructive methods. This allows us to compute…

In the present paper we completely classify locally free sheaves of rank $2$ with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2\times\mathbb{P}^2\subseteq\mathbb{P}^8$ and its general hyperplane…

Let $\pi:X\rightarrow \mathbb{P}^2$ be a K3 surface of genus 2 and $L=\pi^{\ast}\mathcal{O}_{\mathbb{P}^2}(3)$, and assume that $\pi^{\ast}\mathcal{O}_{\mathbb{P}^2}(1)$ is ample as a line bundle on $X$. In this paper, we give a numerical…

On del Pezzo surfaces, we study effective ample $\mathbb{R}$-divisors such that the complements of their supports are isomorphic to $\mathbb{A}^1$-bundles over smooth affine curves.

Let k be an algebraically closed field of characteristic 0. A del Pezzo threefold F with maximal Picard number is isomorphic to P^1xP^1xP^1, where P^1 is the projective line over k. In the present paper we completely classify locally free…

This is the first article in a series aimed at classifying normal del Pezzo surfaces of Picard rank one over algebraically closed fields of arbitrary characteristic up to an isomorphism. Our guiding invariant is the height of a del Pezzo…

To each del Pezzo surface (resp. ruled surface, ruled surface with a section), we describe a natural Lie algebra bundle of type E_n (resp. D_n, A_n) over it. Using lines and rulings on any such surface, we describe various representation…

Given a del Pezzo surface of degree d between 1 and 6, possibly with rational double points, we construct a "tautological" holomorphic G-bundle over X, where G is a reductive group which is an appropriate conformal form of the simply…

An ACM bundle on a polarized algebraic variety is defined as a vector bundle whose intermediate cohomology vanishes. We are interested in ACM bundles of rank one with respect to a very ample line bundle on a K3 surface. In this paper, we…

This paper classifies rank two vector bundles on a del Pezzo threefold $X$ of degree five whose projectivizations are weak Fano. This classification is then used to determine properties of the moduli spaces of such vector bundles on $X$,…

This paper is devoted to the study of a certain class of principal bundles on del Pezzo surfaces, which were introduced and studied by Friedman and Morgan in \cite{FMdP}: The two authors showed that there exists a unique principal bundle…

We study the birational properties of geometrically rational surfaces from a derived categorical point of view. In particular, we give a criterion for the rationality of a del Pezzo surface over an arbitrary field, namely, that its derived…

In this paper, we give a complete classification of initialized and ACM line bundles on a smooth quartic hypersurface on P^3$.

Let $X$ be a smooth quartic hypersurface in $\mathbb{P}^3$. By the Brill-Noether theory of curves on K3 surfaces, if a rank 2 aCM bundle on $X$ is globally generated, then it is the Lazarsfeld-Mukai bundle $E_{C,Z}$ associated with a smooth…

Maximal orders of rank 4 on the projective plane, ramified on a smooth plane quartic are examples of exotic del Pezzo orders. We compute the possible Chern classes for line bundles on such orders and show the moduli space of line bundles…

Working over a perfect field, I classify normal del Pezzo surfaces with base number one that contain a nonrational singularity. They form a huge infinite hierarchy; contractions of ruled surfaces lie on top of it. Descending the hierarchy…