Related papers: Double lines in the quintic del Pezzo fourfold

Let $\mathcal{E}$ be a vector bundle on a smooth projective variety $X\subseteq\mathbb{P}^N$ that is Ulrich with respect to the hyperplane section $H$. In this article, we study the Koszul property of $\mathcal{E}$, the slope-semistability…

The main purpose of this paper is to give an explicit description of the moduli space of semistable sheaves of rank two on a stable curve C obtained by gluing two smooth curves at a point. We prove that the moduli space is irreducible and…

We propose a variation of the classical Hilbert scheme of points - the double nested Hilbert scheme of points - which parametrizes flags of zero-dimensional subschemes whose nesting is dictated by a Young diagram. Over a smooth…

Let X be a nonsingular projective algebraic curve of genus g\ge3. We consider the moduli space M of stable bundles of fixed determinant with rank n and degree d coprime and d>n(2g-2). There is a universal bundle on XxM and we consider the…

One describes those double structures on rational normal curves which are defined scheme theoretically by quadratic equations and have linear syzygies, generalizing this way the double line in the plane

Strongly $\mathbb{Z}$-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras $\mathcal{B}(p;q, 0)$ (over a ring of polynomials in one variable) are…

Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G-bundles on any smooth projective curve over k.

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…

In this note we prove that the moduli space of rank $2n$ symplectic instanton bundles on ${\PP^{2n+1}}$, defined from the well known monad condition, is affine. This result was not known even in the case $n=1$, where the real instanton…

Let X be a projective smooth irreducible polarized variety over the field of complex numbers. Typical examples of wide extensions are vector bundles E that have a subsheaf F whose slope is much bigger than the slope of E/F, and such that F…

We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard…

We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new different constructions, both using line bundles on…

We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP^2. Here, line means a smooth rational curve whose normal bundle is O(1)^2 and the reality implies the invariance under an anti-holomorphic…

A component of the moduli space M_g(Y,b) of stable maps from genus g curves to a variety Y is said to be regular if it is generically smooth and of the expected dimension provided by deformation theory. In this note we prove existence of…

We construct two small resolutions of singularities of the Coble fourfold (the double cover of the four-dimensional projective space branched over the Igusa quartic). We use them to show that all $S_6$-invariant three-dimensional quartics…

We investigate Manin's conjecture for del Pezzo surfaces of degree five with a conic bundle structure, proving matching upper and lower bounds, and the full conjecture in the Galois general case.

We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ to the case of Del Pezzo surfaces of degree 1, where we explicitly…

Given a quadratic two-parameter matrix polynomial in Newton basis $Q_{N} (\lambda ,\mu)$, we construct a vector space of linear two-parameter matrix polynomials and identify a set of linearizations which lie in the vector space. We also…

We study birational geometry of the moduli space of stable sheaves on a quadric surface with Hilbert polynomial $5m + 1$ and $c_{1} = (2, 3)$. We describe a birational map between the moduli space and a projective bundle over a Grassmannian…

We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…