Related papers: Geography of Brill-Noether loci for small slopes

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…

Fix a smooth projetive curve $\mathcal {C}$ of genus $g\geq 2$ and a line bundle $\mathcal{L}$ on $\mathcal{C}$ of degree $d$. Let $M:= \mathcal{SU}_{\mathcal{C}}(r, \mathcal{L})$ be the moduli space of stable vector bundles on…

Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show…

In this article, we classify the irreducible components of moduli stacks of torsion free sheaves of rank 2 on K3 surfaces of Picard number 1. For ruled surfaces, the components of moduli stacks of torsion free sheaves were classified by…

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…

The paper is devoted to highlighting several novel aspects of the moduli space of curves of genus 13, the first genus g where phenomena related to K3 surfaces no longer govern the birational geometry of M_g. We compute the class of the…

The aim of this note is to find upper bounds on the dimension of Brill-Noether locus' inside the moduli space of rank two vector bundles on a smooth algebraic curve. We deduce some consequences of these bounds.

Let H be a semisimple algebaric group and let X be a smooth projective curve defined over an algebraically closed field k. In the first part of this paper we show that the moduli of semistable principal H-bundles exists once given a…

In this paper we obtain bounds on $h^0(E)$ where $E$ is a semistable bundle of rank 3 over a smooth irreducible projective curve $X$ of genus $g \geq 2$ defined over an algebraically closed field of characteristic 0. These bounds are…

For an abelian surface $A$, we consider stable vector bundles on a generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected component of the moduli space which contains the tautological bundles associated to line bundles…

We extend a previous result of Feyzbakhsh concerning the injectivity of a map of moduli spaces and we use this result to construct curves whose Brill-Noether loci have unexpected dimension.

We provide a spectral sequence computing the extension groups of tautological bundles on symmetric products of curves. One main consequence is that, if $E\neq \mathcal O_X$ is simple, then the natural map $\operatorname*{Ext}^1(E,E)\to…

Suppose that the adjusted Brill-Noether number is zero, we prove that there exists a family of twice-marked smooth projective curves such that the family of linear series with two imposed ramification conditions is irreducible. Moreover,…

Let $S$ be a very general smooth hypersurface of degree $6$ in $\mathbb{P}^3$. In this paper we will prove that the moduli space of $\mu$-stable rank $2$ torsion free sheaves with respect to hyperplane section having $c_1 =…

In this paper we begin the classification of coherent systems $(E,V)$ on the projective line which are stable with respect to some value of a parameter $\alpha$. In particular we show that the moduli spaces, if non-empty, are always smooth…

Let $C$ be a smooth, projective, geometrically irreducible curve defined over $\mathbb{R}$ such that $C(\mathbb{R}) = \emptyset$. Let $r>0$ and $d$ be integers which are coprime. Let $L$ be a line bundle on $C$ which corresponds to an…

Fix a smooth projective family of curves $C \to S$ and a split reductive group scheme $G$ over a Noetherian base scheme $S$. For any (possibly nonreduced) fixed relative Cartier divisor $D$, we provide a treatment of the moduli of…

A torsion-free sheaf $E$ on a projective variety $X$ is called quasi-trivial if $E^{\vee\vee}=\mathcal{O}_{X}^{\oplus r}$. While such sheaves are always $\mu$-semistable, they may not be semistable. We study the Gieseker--Maruyama moduli…

Let $C$ be a curve over a non-archimedean local field of characteristic zero. We formulate algebro-geometric statements that imply boundedness of functions on the moduli space of stable bundles of rank $2$ and fixed odd degree determinant…

We produce open subsets of the moduli space of metric graphs without separating edges where the dimensions of Brill-Noether loci are larger than the corresponding Brill-Noether numbers. These graphs also have minimal rank determining sets…