Related papers: Gonality of a general ACM curve in projective 3-sp…

A linear series on a curve C in $P^3$ is "primary" when it does not contain the series cut by planes. We provide a lower bound for the degree of these series, in terms of deg(C), g(C) and of the number $s = min{i: h^0(I_C(i))\neq 0}$; as a…

Let $k$ be an algebraically closed field of characteristic zero, and let $X/k$ be a projective variety. The conjectures of Demailly--Green--Griffiths--Lang posit that every integral subvariety of $X$ is of general type if and only if $X$ is…

Let $C$ be a smooth irreducible complex projective curve of genus $g \geq 2$ and $M$ the moduli space of stable vector bundles on $C$ of rank $n$ and degree $d$ with $\gcd(n,d)=1$. A generalised Picard sheaf is the direct image on $M$ of…

We study the Clifford dimension of an integral curve. To do so, we extend the notion of Clifford index, allowing torsion-free sheaves on its computation. We derive results for arbitrary curves, and then focus on the monomial case. In this…

We prove that in the moduli space of genus-g metric graphs the locus of graphs with gonality at most d has the classical dimension min{3g-3,2g+2d-5}. This follows from a careful parameter count to establish the upper bound and a…

Let $C$ be an irreducible, reduced, non-degenerate curve, of arithmetic genus $g$ and degree $d$, in the projective space $\mathbf P^4$ over the complex field. Assume that $C$ satisfies the following {\it flag condition of type $(s,t)$}:…

Let G be a connected reductive algebraic group and H be a reductive closed and connected subgroup of G both defined on an algebraically closed field of characteristic zero. We consider the set C of the couple (x,y) of the dominant weights…

Let $k$ be an algebraically closed field and let $C$ be a non--hyperelliptic smooth projective curve of genus $g$ defined over $k$. Since the canonical model of $C$ is arithmetically Gorenstein, Macaulay's theory of inverse systems allows…

In this paper we partially address two issues: - The first is a rigidity property for pairs (S,C) consisting of a general projective K3 surface S, and a curve C obtained as the normalization of a nodal, hyperplane section of S. We prove…

Given a smooth non-hyperelliptic curve C of genus 3 and a maximal isotropic subgroup (w.r.t. the Weil pairing) L in Jac(C)[2], there exists a smooth curve C' s.t. Jac(C')=Jac(C)/L. This construction is symmetric. i.e. if we start with C'…

We consider a variant of metrised graphs where the edge lengths take values in a commutative monoid, as a higher-rank generalisation of the notion of a tropical curve. Divisorial gonality, which Baker and Norine defined on combinatorial…

Given n general points p_1, p_2,..., p_n \in P^r, it is natural to ask whether there is a curve of given degree d and genus g passing through them; by counting dimensions a natural conjecture is that such a curve exists if and only if \[n…

In this work, we investigate the behaviour of the covering gonality of a very general hypersurface in a product of projective spaces. Inspired by the work of Bastianelli, Ciliberto, Flamini and Suppino in [BCFS19] which addresses the case…

We study the syzygies of projections of elliptic normal curves. Let $C \subset \mathbb{P}^{d-1}$ be an elliptic normal curve of degree $d \ge 5$, and let $C_q$ denote the projection of $C$ from a point $q$. We obtain sharp bounds for the…

Let C be a smooth projective curve over a discretely valued field K, defined by an affine equation f(x,y)=0. We construct a model of C over the ring of integers of K using a toroidal embedding associated to the Newton polygon of f. We show…

Let $C$ be a smooth curve with gonality $k\ge 6$ and genus $g\ge 2k^2+5k-6$. We prove that $W^1_d({C})$ has the expected dimension and that the general element of any irreducible component of $W^1_d({C})$ is primitive if either $g-k+4\le…

Let $C$ be an integral projective nodal curve over $\mathbb C$, of arithmetic genus $g \geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$ and degree $e$. Let $\textrm{Quot}_{C/\mathbb C}(E,k,d)$ denote the Quot scheme of quotients…

We prove that a smooth, complex plane curve $C$ of odd degree can be defined by a polynomial with real coefficients if and only if $C$ is isomorphic to its complex conjugate. Counterexamples are known for curves of even degree. More…

Given a connected smooth projective surface X over the complex numbers, together with a simple normal crossings divisor D on it, we study finite normal covers Y of X that are unramified outside D. Given moreover a fibration of X onto a…

We study the family of irreducible curves with $\delta$ nodes belonging to a free linear system $|C|$ with smooth general member on a surface $S$ such that $|K_S|$ is ample. Under the assumption that $C$ is numerically equivalent to $pK_S$,…