Related papers: Aller-retour vers l'inseparable

The aim of this paper is to classify reduction types of algebraic curves. Reduction types capture the discrete invariants of fibres in one-dimensional families of curves, and they have been described in genus 1, 2 and 3. For fixed genus…

This article describes the geometry of isomorphisms between complements of geometrically irreducible closed curves in the affine plane $\mathbb{A}^2$, over an arbitrary field, which do not extend to an automorphism of $\mathbb{A}^2$. We…

We study the "generic" degenerations of curves with two singular points when the points merge. First, the notion of generic degeneration is defined precisely. Then a method to classify the possible results of generic degenerations is…

Let $X$ (resp. $Y$) be a curve of genus 1 (resp. 2) over a base field $k$ whose characteristic does not equal 2. We give criteria for the existence of a curve $Z$ over $k$ whose Jacobian is up to twist (2,2,2)-isogenous to the products of…

We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author's PhD thesis are also included.

We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.

We show that certain groups of piecewise linear homeomorphims of the interval are invariably generated.

We investigate the quadratic descent of totally decomposable algebras with involution of orthogonal type in characteristic two. Both separable and inseparable extensions are included.

We use the theory of p-curvature of connections to analyze stable vector bundles of rank 2 on curves of genus 2 which pull back to unstable bundles under the Frobenius morphism. We take two approaches, first using explicit formulas for…

Looking in positive characteristic for failures of the Bertini-Sard theorem, we determine, up to birational equivalence, the separable proper morphisms of smooth algebraic varieties in characteristic two, whose fibres are non-smooth curves…

We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…

In this paper, we develop the theory of flashes of an algebraic curve. We show that the theory is birationally invariant in a sense which we will make more precise below. We also show how the theory provides a foundation for the method of…

In this paper we characterize the irreducible curves lying in $C^{(2)}$. We prove that a curve $B$ has a degree one morphism to $C^{(2)}$ with image a curve of degree $d$ with irreducible preimage in $C\times C$ if and only if there exists…

A curve is called nondegenerate if it can be modeled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We show that up to genus 4, every curve is nondegenerate. We also prove that the locus of nondegenerate…

We classify endomorphisms of the plane that preserve a pencil of curves.

We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.

We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.

We obtain a minimal generating set of involutions for the level 2 subgroup of the mapping class group of a closed nonorientable surface.

We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…

Given smooth, projective, geometrically integral algebraic curves $X$ and $Y$ defined over a number field $K$, assuming that there is a non-constant $K$-morphism $\varphi \colon X \to Y$, we give an upper bound on the minimum of the degrees…