Related papers: Aller-retour vers l'inseparable

We show that given a dominant morphism between two smooth varieties of the same dimension, the induced morphism between the formal neighborhoods of two arcs on these varieties is a closed embedding, of codimension given by the order of…

In a previous paper, we proved that over a finite field $k$ of sufficiently large cardinality, all curves of genus at most 3 over k can be modeled by a bivariate Laurent polynomial that is nondegenerate with respect to its Newton polytope.…

Globally irreducible nodes (i.e. nodes whose branches belong to the same irreducible component) have mild effects on the most common topological invariants of an algebraic curve. In other words, adding a globally irreducible node (simple…

In this paper we extend a previous investigation by us regarding an iterative construction of irreducible polynomials over finite fields of odd characteristic. In particular, we show how it is possible to iteratively construct irreducible…

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.

Two (proper) colorings of a graph are adjacent if they differ on exactly one vertex. Jerrum proved that any $(d + 2)$-coloring of any d-degenerate graph can be transformed into any other via a sequence of adjacent colorings. A result of…

We answer a question posed by Love asking about a correspondence between isogenies from a supersingular elliptic curve to its Frobenius base-change and rank-2 sublattices of its Gross lattice. We recast the question as one about the…

We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…

An updated proof of a 1933 theorem of Goeritz, exhibiting a finite set of generators for the group of automorphisms of the 3-sphere that preserve a genus two Heegaard splitting. The group is analyzed via its action on a certain connected…

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of…

We construct a family of plane curves as pull-backs of a conic for abelian coverings of P^2. If the conic is tangent to the ramification lines one obtains a family of curves of degree 2n with 3n singularities of type A_{n-1}. We calculate…

We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian.

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…

We construct connected $2$-arc-transitive covers of the Petersen graph with non-solvable transformation groups, solving the long-standing problem for the existence of such covers.

We compute the algebra of differential invariants of unparametrized curves in the homogeneous G(2) flag varieties, namely in G(2)/P. This gives a solution to the equivalence problem for such curves. We consider the cases of integral and…

Let f = 0 be an implicit singular plane curve. When deforming f = 0, inflections and vertex emerge from the singularities. In this papper, we classify the deformations of f = 0 with respect to the inflections and the vertices in the cases…

A graph is 2-degenerate if every subgraph contains a vertex of degree at most 2. We show that every 2-degenerate graph can be drawn with straight lines such that the drawing decomposes into 4 plane forests. Therefore, the geometric…

We construct three families of pairs of genus 2 curves over a field K, whose Jacobians are isomorphic as unpolarized abelian varieties. Each family is parameterized by an open subset of the Projective line over K. Our construction is based…

We construct embeddings of surface groups into the group of germs of analytic diffeomorphisms in one variable.

We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…