Related papers: Wall-crossing of universal Brill-Noether classes

We study the stable hyperelliptic locus, i.e. the closure, in the Deligne- Mumford moduli space of stable curves, of the locus of smooth hyperelliptic curves. Working on a suitable blowup of the relative Hilbert scheme (of degree 2)…

Let (S,H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c_1(E),H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether…

The classical Brill-Noether theorem states that a map from a general curve to a projective space deforms in a family of expected dimension as long as its image does not lie in any hyperplane. In this note, we observe, as a direct…

We prove that the Gieseker moduli space of stable sheaves on a smooth projective threefold $X$ of Picard rank 1 is separated from the moduli space of PT stable objects by a single wall in the space of Bridgeland stability conditions on $X$,…

Let us consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. Since the Brill-Noether number is equal to -2, such a locus has codimension two. Using the method of test surfaces, we compute…

Our purpose in this paper is to construct new examples of twisted Brill-Noether loci on curves of genus $g\ge2$. Many of these examples have negative expected dimension. We deduce also the existence of a new region in the Brill-Noether map,…

When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on $R^3 \times S^1$ are strikingly similar and, to a large extent, dictated by…

We study normal crossings compactifications of the moduli space of maps $\mathcal{M}_{g, n}(\mathbb{P}^r, d)$, for $g = 0$ and $g = 1$. In each case we explicitly determine the dual boundary complex, and prove that it admits a natural…

In this paper, we compute the number of general points through which a general Brill-Noether curve in $\mathbb{P}^4$ passes. We also prove an analogous theorem when some points are constrained to lie in a transverse hyperplane. As explained…

We develop a novel approach to the Brill-Noether theory of curves endowed with a degree k cover of the projective line via Bridgeland stability conditions on elliptic K3 surfaces. We first develop the Brill-Noether theory on elliptic K3…

We show that the wall-crossing in Bridgeland stability fails to be detected by the birational geometry of stable sheaves, and vice versa. There is a wall in the stability space of canonical genus four curves which does not induce a step in…

Let $X$ be a non-singular algebraic curve of genus $g$. We prove that the Brill-Noether locus $\bns $ is non-empty if $d= nd' +d'' $ with $0< d'' <2n$, $1\le s\le g$, $d'\geq (s-1)(s+g)/s $, $n\leq d''+(n-k)g$, $(d'',k)\ne(n,n)$. These…

Let $v_d(\mathbb{P}^2)\subset |\mathcal{O}_{\mathbb{P}^2}(d)|$ denote the $d$-uple Veronese surface. After studying some general aspects of the wall-crossing phenomena for stability conditions on surfaces, we are able to describe a sequence…

In this note we give an easy proof of the existence of generically smooth components of the expected dimension of certain Brill--Noether loci of stable rank 2 vector bundles on a curve with general moduli, with related applications to…

In this paper, we give a simple description of the deformations of a map between two smooth curves with partially prescribed branching, in the cases that both curves are fixed, and that the source is allowed to vary. Both descriptions work…

In this paper we study the Brill-Noether theory of sub-line bundles of a general, stable rank-two vector bundle on a curve C with general moduli. We relate this theory to the geometry of unisecant curves on smooth, non-special scrolls with…

For a projective nonsingular curve of genus $g$, the Brill-Noether locus $W^r_d(C)$ parametrizes line bundles of degree $d$ over $C$ with at least $r+1$ sections. When the curve is generic and the Brill-Noether number $\rho(g,r,d)$ equals…

Let $\M_g$ be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $\rho(g,1,n)$ is non-negative the Petri locus $P^1_{g,n}\subset \M_g$ has a divisorial component whose…

We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum…

We prove that the pullbacks of the virtual fundamental classes of the Brill-Noether loci under any Abel-Jacobi section lie in the tautological ring of the moduli space of stable curves. This resolves a conjecture of Pagani, Ricolfi and van…