Related papers: Self-self-dual spaces of polynomials

A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this paper we prove that the same holds for involutions under…

A self-dual map $G$ is said to be \emph{antipodally self-dual} if the dual map $G^*$ is antipodal embedded in $\mathbb{S}^2$ with respect to $G$. In this paper, we investigate necessary and/or sufficient conditions for a map to be…

Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical…

Let T be a torus over an algebraically closed field k of characteristic 0, and consider a projective T-module P(V). We determine when a projective toric subvariety X of P(V) is self-dual, in terms of the configuration of weights of V.

We present self-dual N=2 supergravity in superspace for Euclidean seven dimensions with the reduced holonomy G_2 \subset SO(7), including all higher-order terms. As its foundation, we first establish N=2 supergravity without self-duality in…

Given a point-line geometry P and a pappian projective space S,a veronesean embedding of P in S is an injective map e from the point-set of P to the set of points of S mapping the lines of P onto non-singular conics of S and such that e(P)…

We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d+3 vertices. This…

The moduli space M_0 of semi-stable rank 2 vector bundles with fixed trivial determinant over a non-hyperelliptic curve C of genus 3 is isomorphic to a quartic hypersurface in P^7 (Coble's quartic). We show that M_0 is self-dual and that…

We consider self-dual metrics on 3CP^2 of positive scalar curvature admitting a non-trivial Killing field, but which is not conformally isometric to LeBrun's metrics. Firstly, we determine defining equations of the twistor spaces of such…

We discover a class of projective self-dual algebraic varieties. Namely, we consider actions of isotropy groups of complex symmetric spaces on the projectivized nilpotent varieties of isotropy modules. For them, we classify all orbit…

Let $F$ be a field of characteristic zero and let $E$ be the Grassmann algebra of an infinite dimensional $F$-vector space $L$. In this paper we study the superalgebra structures (that is the $\mathbb{Z}_{2}$-gradings) that the algebra $E$…

Using (partial) curvature flows and the transitive action of subgroups of O(d,Z) on the indices {1,...,d} of the components of the Yang-Mills curvature in an orthonormal basis, we obtain a nested system of equations in successively higher…

Let V be a finite dimensional representation of the connected complex reductive group H. Denote by G the derived subgroup of H and assume that the categorical quotient of V by G is one dimensional. In this situation there exists a…

We introduce a notion of ``$n$-dual'' to a simplicial vector space for $n\ge 0$. Coming with it, there is a canonical pairing, which we show to be non-degenerate up to homotopy for homotopy $n$-types. As a result this notion of duality is…

Let us say that a curve $C\subset\mathbb P^3$ is osculating self-dual if it is projectively equivalent to the curve in the dual space $(\mathbb P^3)^*$ whose points are osculating planes to~$C$. Similarly, we say that a $k$-dimensional…

The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group $G$ of degree $n$ there exists a doubly-even self-dual $G$-invariant code if and only…

We investigate the class of root systems $R$ obtained by extending an $A_1$-type irreducible root system by a free abelian group $G$. In this context there is a Weyl group $W$ and a group $U$ with the presentation by conjugation. Both…

A lattice polytope $\mathcal{P}$ is called reflexive if its dual $\mathcal{P}^\vee$ is a lattice polytope. The property that $\mathcal{P}$ is unimodularly equivalent to $\mathcal{P}^\vee$ does not hold in general, and in fact there are few…

Self-dual configurations of 2n points in a projective space of dimension n-1 were studied by Coble, Dolgachev-Ortland, and Eisenbud-Popescu. We examine the self-dual matroids and self-dual valuated matroids defined by such configurations,…

Let $V$ be an $n$-dimensional left vector space over a division ring $R$ and $n\ge 3$. Denote by ${\mathcal G}_{k}$ the Grassmann space of $k$-dimensional subspaces of $V$ and put ${\mathfrak G}_{k}$ for the set of all pairs $(S,U)\in…