Related papers: Non-globally generated bundles on curves

Let V^{r}_{d,g, \delta} be the Hilbert scheme of nodal curves in P^r of degree d and arithmetic genus g with \delta nodes. Under suitable numerical assumptions on d and g, for every 0 \le \delta \le g we construct an irreducible component…

In this paper, we study special generalized null correlation bundles on $\mathbb{P}^{5}$. We prove that special generalized null correlation bundles on $\mathbb{P}^{5}$ are stable under some numerical conditions. Moreover, we prove that the…

It is well-known that a minimal graph of codimension one is stable, i.e. the second variation of the area functional is non-negative. This is no longer true for higher codimensional minimal graphs. In this note, we prove that a minimal…

Let $C$ be a smooth projective curve of genus $g>0$. We describe an open locus of Bridgeland stability conditions on the bounded derived category of coherent systems on $C$, and show that stability manifold detects the Brill--Noether theory…

We study families of ropes of any codimension that are supported on lines. In particular, this includes all non-reduced curves of degree two. We construct suitable smooth parameter spaces and conclude that all ropes of fixed degree and…

In this paper we proof the existence of a linearization for singular principal G-bundles not depending on the base curve. This allow us to construct the relative compact moduli space of {\delta}-(semi)stable singular principal G-bundles…

We study stable rank 2 vector bundles with trivial determinant whose Frobenius pull back is non stable over a general curve of genus g>1. In genus 2, we apply recent results about the theta divisor associated to the bundle B of locally…

In the first part of this paper, we discuss the notion of irreducibility of cycles in the moduli spaces of n-marked rational tropical curves. We prove that Psi-classes and vital divisors are irreducible, and that locally irreducible…

Let $X$ be a smooth projective curve of genus $g\geq 2$ over an algebraically closed field $k$ of characteristic $p>0$, $F_X:X\rightarrow X$ the absolute Frobenius morphism. Let $\M^s_X(r,d)$ be the moduli space of stable vector bundles of…

This note revisits stability conditions on the bounded derived categories of coherent sheaves on irreducible projective curves. In particular, all stability conditions on smooth curves are classified and a connected component of the…

We bound the codimension of components of the nonabelian Hodge loci in the relative de Rham moduli space over $\shm_{g,n}$ in terms of the rank and level of a complex variation of Hodge structure. If the rank is $r$ and the level is $\ell$,…

Let $C$ be an irreducible smooth projective curve of genus $g\geq 2$ over an algebraically closed field. We prove that the moduli stack of semi-stable vector bundles on $C$ of fixed rank and determinant is $\mathbb{A}^1$--connected. We also…

In this paper, we study some aspects of the irreducibility of $\widetilde{M_g^{Pl}(G)}$ and its interrelation with the existence of "normal forms", i.e. non-singular plane equations (depending on a set of parameters) such that a…

Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to…

In this paper we study the irreducible components of the compactified Jacobian of a ribbon $X$ of arithmetic genus $g$ over a smooth curve $X_{\mathrm{red}}$ of genus $\bar{g}$. We prove that when $g\geq 4\bar{g}-2$ the moduli space of rank…

Given a rank $r$ stable bundle over a smooth irreducible projective curve $C,$ there is an associated rank $2r$ bundle over $S^2(C),$ the second symmetric power of $C.$ In this article we study the stability of this bundle. As a consequence…

We describe new irreducible components of the moduli space of rank $2$ semistable torsion free sheaves on the three-dimensional projective space whose generic point corresponds to non-locally free sheaves whose singular locus is either…

In this paper, we study double structures supported on rational normal curves. After recalling the general construction of double structures supported on a smooth curve described in \cite{fer}, we specialize it to double structures on…

We study the derived category of the moduli space $SU_C(2)$ of rank $2$ vector bundles on a smooth projective curve $C$ of genus $g\ge 2$ with trivial determinant. This generalizes the recent work by Tevelev and Torres on the case with…

In this paper, we prove that for any smooth projective curve $C$ of genus $g\geq2$ over an algebraically closed field of positive characteristic, there exists a stable vector bundle over $C$ whose exterior power is not semi-stable.