Related papers: Moh's example of algebroid space curves
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…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
One can consider the Hilbert scheme as a natural compactification of the space of smooth projective curves with fixed Hilbert polynomial. Here we consider a different modular compactification, namely the functor CM parameterizing curves…
A regular nilpotent Hessenberg Schubert cell is the intersection of a regular nilpotent Hessenberg variety with a Schubert cell. In this paper, we describe a set of minimal generators of the defining ideal of a regular nilpotent Hessenberg…
In this article, we introduce the concepts of excision and idealization for a multiplicative Lie algebra (also for a Lie algebra), which provides two new multiplicative Lie algebras (or Lie algebras) from a given multiplicative Lie algebra…
We construct an example of an $A_{\infty}$ algebra structure defined over a finite dimensional graded vector space.
We present an algorithm to compute the automorphism group of a Mori dream space. As an example calculation, we determine the automorphism groups of singular cubic surfaces with general parameters. The strategy is to study graded…
In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify…
We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds…
An affine variety induces the structure of an algebraic matroid on the set of coordinates of the ambient space. The matroid has two natural decorations: a circuit polynomial attached to each circuit, and the degree of the projection map to…
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…
This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of "Algebraic Multi-Grid", but it…
Using families of curves to generalize vector fields, the Lie bracket is defined on a metric space, M. For M complete, versions of the local and global Frobenius theorems hold, and flows are shown to commute if and only if their bracket is…
In this article, we provide an explicit description of a set of generators for any ideal of an ultragraph Leavitt path algebra. We provide several additional consequences of this description, including information about generating sets for…
The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the…
We extend the work of Cremona, Fisher and Stoll on minimising genus one curves of degrees 2,3,4,5, to some of the other representations associated to genus one curves, as studied by Bhargava and Ho. Specifically we describe algorithms for…
Let V be an infinite-dimensional vector space over a field of characteristic not equal to 2. We classify ideals of the Lie algebra gl(V) of all linear transformations of the space V.
We prove an existence theorem for good moduli spaces, and use it to construct the second flip in the log minimal model program for the moduli space of stable curves. In fact, our methods give a uniform, self-contained construction of the…
In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime…
We establish formulas for the Hilbert series of the Chow ring of a polymatroid using arbitrary building sets. For braid matroids and minimal building sets, our results produce new formulas for the Poincar\'e polynomial of the moduli space…