Related papers: Brill-Noether loci
We briefly survey recent results related to linear series on curves that are general in various moduli spaces, highlighting the interplay between algebraic geometry on a general curve and the combinatorics of its degenerations.…
For a generic compact Riemann surface the theta function is at every point on the Jacobian equal to its first Taylor term, up to a holomorphic change of local coordinates and multiplication by a local holomorphic unit. More generally, any…
Continuing our previous study of modified expected dimensions for rank-2 Brill-Noether loci with prescribed special determinants, we introduce a general framework which applies a priori for arbitrary rank, and use it to prove modified…
Denote by ${\mathcal P}_{g,d}^{r,k}$ the subset of the moduli space of curves of genus g consisting of those curves that have a linear series of degree d and dimension r for which the Petri map has kernel of dimension at least k. We show…
In the 1990's, Bertram, Feinberg and Mukai examined Brill-Noether loci for vector bundles of rank 2 with fixed canonical determinant, noting that the dimension was always bigger in this case than the naive expectation. We generalize their…
Given a family $\pi:\mc{X} \rightarrow B$ of smooth projective varieties, a closed fiber $\mc{X}_o$ and an invertible sheaf $\mc{L}$ on $\mc{X}_o$, we compare the Hodge locus in $B$ corresponding to the Hodge class $c_1(\mc{L})$ with the…
For genus $g = \frac{r(r+1)}{2}+1$, we prove that via the forgetful map, the universal Prym-Brill-Noether locus $\mathcal{R}^r_g$ has a unique irreducible component dominating the moduli space $\mathcal{R}_g$ of Prym curves.
The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and…
Brill-Noether theory of curves has played a crucial role in the study of curves and their moduli since the 19th century, and has been extensively studied by several authors. Clifford's theorem provides a starting point in determining the…
For a general curve C of genus $g\geq 10$, we show that the Brill- Noether locus $B^4(2,K_C)$ contains irreducible sub-varieties $B_3\supset B_4 \supset \cdots \supset B_n$, where $B_n$ is of dimension $3g-10-n$ and $B_3$ is an irreducible…
We study Brill-Noether loci of three kinds of spectral curves: classical spectral curves as introduced by Hitchin, spectral curves over the projective line and double covers whose branch locus is a canonical divisor. Our techniques are…
We establish two-pointed Prym-Brill-Noether loci with special vanishing at two points, and determine their K-theory classes when the dimensions are as expected. The classes are derived by the applications of a formula for the K-theory of…
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 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…
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 prove that a certain Brill-Noether locus over a non-hyperelliptic curve $C$ of genus 4, is isomorphic to the \textit{Donagi-Izadi cubic threefold} in the case when the pencils of the two trigonal line bundles of $C$ coincide.
We show that the space of linear series of certain multi-degree (including the balanced ones) and rank $r$ on a general binary curve has the expected dimension if nonempty. This generalizes Theorem 24 of Caporaso's paper about binary curves…
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…
In this paper, we consider higher rank Brill-Noether theory for smooth curves of genus 5, obtaining new upper bounds for non-emptiness of Brill-Noether loci and many new examples.
In this paper we determine the number of general points through which a Brill--Noether curve of fixed degree and genus in any projective space can be passed.