Related papers: Minimalit\'e des courbes sous-canoniques

We study sheaves E on a smooth projective curve X which are minimal with respect to the property that $h^0(E \otimes L) >0$ for all line bundles L of degree zero. We show that these sheaves define ample divisors D(E) on the Picard torus…

We characterize the curves in $ P^3$ which are minimal in their biliaison class. Such curves are exactly the curves which do no admit an elementary descending biliaison. As a consequence we have that every curve in $P^3$ can be obtained…

Let $A$ be a local noetherian ring and $N$ be a locally sheaf on the projective space $P^3_A$ : one proves easily that there exists a family $C$ of (smooth connected) curves contained in $P^3_A$, flat over $A$, and an integer $h$ such that…

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…

This paper is the text of a lecture given at the Catania conference on Commutative Algebra and Algebraic Geometry, in honor of the 60th birthday of Silvio Greco. It analyses the correspondences between equivalence classes of objects related…

We consider the set E of curves with positive algebraic curvature, whose extremities and tangents in their extremities are given. For each of the curves of E, we define the minimum of the radius of curvature. We first prove that there…

The purpose of this paper is to study minimal monads associated to a rank two vector bundle $\mathcal E$ on $\mathbb P^n$. In particular, we study situations where $\mathcal E$ has $H^i_*(\mathcal E) =0$ for $1<i<n-1$, except for one pair…

Let $C\subset \mathbb{P}^n$ be a rational normal curve and let $\ell_O:\mathbb{P}^{n+1}\dashrightarrow \mathbb{P}^n$ be any tangential projection form a point $O\in T_AC$ where $A\in C$. Hence $X:= \ell_O(C)\subset \mathbb{P}^n$ is a…

A viable and still unproved conjecture states that, if $X$ is a smooth algebraic surface and $C$ is a smooth algebraic curve in $X$, then $C$ realizes the smallest possible genus amongst all smoothly embedded $2$-manifolds in its homology…

In this paper we investigate an arithmetic analogue of the gonality of a smooth projective curve $C$ over a number field $k$: the minimal $e$ such there are infinitely many points $P \in C(\bar{k})$ with $[k(P):k] \leq e$. Developing…

Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under…

We restate the semistable reduction theorem from geometric invariant theory in the context of spaces of morphisms on $\mathbb{P}^{n}$. For every complete curve $C$ downstairs, we get a $\mathbb{P}^{n}$-bundle on an abstract curve $D$…

A point $p$ on a smooth complex projective curve $C$ of genus $g>3$ is subcanonical if the divisor $(2g-2)p$ is canonical. In the moduli space of pointed curves, the subcanonical locus is described by pairs $(C,p)$ as above, and it consists…

We prove here the following results: \begin{th} Let $E$ a rank 2 vector bundle over ${\bf P}_3$, if $C$ is a reduced irreducible curve of ${\bf P}_3^{\vee}$ such that $E_H$ is unstable for all $H\in C$ then $C$ is a line. \end{th} We define…

We consider the set E of curves with positive algebraic curvature, whose extremities and tangents in their extremities are given. For each of the curves of E, we define the minimum of the radius of curvature. There exists a unique curve of…

A triangulation of a circle bundle $ E \xrightarrow[\text{}]{\pi} B$ is a triangulation of the total space $E$ and the base $B$ such that the projection $\pi$ is a simplicial map. In the paper we address the following questions: Which…

In this short note, we show that any rational curve passing through the generic point in a moduli space of stable bundles with rank $r$ and fixed determinant on a smooth projective curve of genus $g\ge 4$ has degree (with respect to the…

Let $E/\mathbb{Q}$ be an elliptic curve. The reduced minimal model of $E$ is a global minimal model $y^{2}+a_{1}xy+a_{3}y=x^{3}+a_{2}x^{2}+a_{4}x+a_{6}$ which satisfies the additional conditions that $a_{1},a_{3}\in \{0,1\}$ and…

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…

For any admissible subcategory of the bounded derived category of coherent sheaves on a smooth proper variety, we prove that sections of the canonical bundle impose a strong constraint on the supports of the objects of the subcategory or…