• Corpus ID: 232427866

A moduli interpretation of untwisted binary cubic forms

  title={A moduli interpretation of untwisted binary cubic forms},
  author={Rajesh S. Kulkarni and Charlotte Ure},
We give a moduli interpretation to the quotient of (nondegenerate) binary cubic forms with respect to the natural GL2-action on the variables. In particular, we show that these GL2 orbits are in bijection with pairs of j-invariant 0 elliptic curves together with 3-torsion Brauer classes that are invariant under complex multiplication. The binary cubic generic Clifford algebra plays a key role in the construction of this correspondence. Introduction The subject of homogeneous forms has… 

On the equivalence of binary cubic forms

. We consider the question of determining whether two binary cubic forms over an arbitrary field K whose characteristic is not 2 or 3 are equivalent under the actions of either GL(2 ,K ) or SL(2 ,K ),



The extension of the reduced Clifford algebra and its Brauer class

AbstractThe shape Clifford algebraCf of a binary form f of degree d is the k-algebra k{x,y}/I, where I is the ideal generated by {(αx+βy)d−f(α,β)∥α,βk}. Cf has a natural homomorphic image Af, called

Rings and ideals parameterized by binary n‐ic forms

  • M. Wood
  • Mathematics
    J. Lond. Math. Soc.
  • 2011
This paper shows exactly what algebraic structures are parametrized by binary n-ic forms, and proves these parametrizations when any base scheme replaces the integers, and shows that the correspondences between forms and the algebraic data are functorial in the base scheme.

A Note on Generic Clifford Algebras of Binary Cubic Forms

We study the representation theoretic results of the binary cubic generic Clifford algebra C $\mathcal C$ , which is an Artin-Schelter regular algebra of global dimension five. In particular, we show

On the Clifford algebra of a binary form

The Clifford algebra Cj of a binary form f of degree d is the k-algebra k{x,y}/I, where I is the ideal generated by {(ax + βy) d - f(α, β) | α, β E k}. C f has a natural homomorphic image A f that is

Arithmetic invariant theory

Let k be a field, let G be a reductive algebraic group over k, and let V be a linear representation of G. Geometric invariant theory involves the study of the k-algebra of G-invariant polynomials on

Linearizing of n-ic forms and generalized Clifford algebras

A homogeneous form fd(x1,…,xn) of degree d with coefficients in a field F has a finite linearization if for some m there are m×m matrices α1,…,αn with entries in F so that is the identity matrix.

Relative Brauer groups of genus 1 curves

In this paper we develop techniques for computing the relative Brauer group of curves, focusing particularly on the case where the genus is 1. We use these techniques to show that the relative Brauer

Crossed Products and Hereditary Orders

Let S be the integral closure of a discrete rank one valuation ring R in a finite Galois extension of the quotient field of R, and denote the Galois group of the quotient field extension by G. It has


§1.1. Motivation. The purpose of these notes is to explain the definition and basic properties of the Néron model A of an abelian variety A over a global or local field K. We also give some idea of

When is the Clifford algebra of a binary cubic form split