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There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290;…

Given a $2^N$-dimensional Cayley-Dickson algebra, where $3 \leq N \leq 6$, we first observe that the multiplication table of its imaginary units $e_a$, $1 \leq a \leq 2^N -1$, is encoded in the properties of the projective space PG$(N-1,2)$…

We completely describe the higher secant dimensions of all connected homogeneous projective varieties of dimension at most 3, in all possible equivariant embeddings. In particular, we calculate these dimensions for all Segre-Veronese…

We consider surjective endomorphisms f of degree > 1 on the projective n-space with n = 3, and f^{-1}-stable hypersurfaces V. We show that V is a hyperplane (i.e., deg(V) = 1) but with four possible exceptions; it is conjectured that deg(V)…

Recently, using the model of N=2 supergravity -- vector multiplets interaction with the scalar field geometry $SU(1,m)/SU(m)\otimes U(1)$ as an example, we have shown that even when the scalar field geometry is fixed, one can have a whole…

We introduce an axiom on strong parapolar spaces of diameter 2, which arises naturally in the framework of Hjelmslev geometries. This way, we characterize the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain half-spin…

A 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold is constructed. It parametrizes the stable rank 2 vector bundles on the hypeplane sections of the cubic 4-fold which are obtained by Serre's construction from…

We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…

In the context of N=2 supergravity we explain the occurrence of partial super-Higgs with vanishing vacuum energy and moduli stabilization in a model suggested by superstring compactifications on type IIB orientifolds with 3-form fluxes. The…

In this paper we study a family of scattered $\F_q$--linear sets of rank $tn$ of the projective space $PG(2n-1,q^t)$ ($n \geq 1$, $t\geq 3$), called of {\it pseudoregulus type}, generalizing results contained in [G. Marino, O. Polverino, R.…

Let $G$ be a reductive linear algebraic group. The simplest example of a projective homogeneous $G$-variety in characteristic $p$, not isomorphic to a flag variety, is the divisor $x_0 y_0^p+x_1 y_1^p+x_2 y_2^p=0$ in $P^2\times P^2$, which…

We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to…

For essential reduced hyperplane arrangements of 4 variables, we show that the pole order spectral sequence degenerates almost at $E_2$, and completely at $E_3$, generalizing the 3 variable case where the complete $E_2$-degeneration is…

We study associative submanifolds of the Berger space SO(5)/SO(3) endowed with its homogeneous nearly-parallel G2-structure. We focus on two geometrically interesting classes: the ruled associatives, and the associatives with special Gauss…

We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For…

Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann…

This paper is concerned with polynomially generated multiplier invariant subspaces of the weighted Bergman space $A_{\boldsymbol{\beta}}^2$ in infinitely many variables. We completely classify these invariant subspaces under the unitary…

We present a class of classically marginal N-vector models in d=4 and d=3, whose scalar potentials can be written as subdeterminants of symmetric matrices. The d=3 case is a generalization of the scalar Bagger-Lambert-Gustavsson (BLG)…

We classify the supersymmetric solutions of ungauged N=1 d=5 SUGRA coupled to vector multiplets and hypermultiplets. All the solutions can be seen as deformations of solutions with frozen hyperscalars. We show explicitly how the…

Let $F$ be a $p$-adic field and $(\pi, V)$ an irreducible complex representation of $G=GSp(4, F)$ with trivial central character. Let ${\rm Si}(\mathfrak{p}^2)\subset G$ denote the Siegel congruence subgroup of level $\mathfrak{p}^2$ and…