Related papers: On MPS construction of blocking sets in projective…
In this paper, we shall generalize the theory of mixed Hodge structures due to Deligne and obtain a subcategory GMHS in the category of mixed Hodge structures such that we have Ext_{GMHS}^2(Q,-)\not=0 in general.
The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the real points of the moduli space of distinct points on the projective line as an open dense subset.…
We describe in detail a general scheme for embedding several BPS monopoles into a theory with a larger gauge group, which generalizes embeddings of SU(2) monopoles discussed by several authors. This construction is applied to obtain…
We provide a characterisation of $(n-1)$-spreads in $\mathrm{PG}(rn-1,q)$ that have $r$ normal elements in general position. In the same way, we obtain a geometric characterisation of Desarguesian $(n-1)$-spreads in $\mathrm{PG}(rn-1,q)$,…
We construct general static black hole configuration for the theory of N=2, d=5 supergravity coupled to an arbitrary number of Abelian vector multiplets. The underlying very special geometry structure plays a major role in this…
We give a survey on projective ring lines and some of their substructures which in turn are more general than a projective line over a ring.
By way of intersection theory on $\bar M_{g,n}$, we show that geometric interpretations for conformal blocks, as sections of ample line bundles over projective varieties, do not have to hold at points on the boundary. We show such a…
We continue our study of BPS equations and supersymmetric configurations in the Bagger-Lambert theory. The superalgebra allows three different types of central extensions which correspond to compounds of various M-theory objects: M2-branes,…
Strong blocking sets, introduced first in 2011 in connection with saturating sets, have recently gained a lot of attention due to their correspondence with minimal codes. In this paper, we dig into the geometry of the concatenation method,…
The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,\lambda)$ design. We find the parameters of…
The projective space of order $n$ over the finite field $\Fq$, denoted here as $\Ps$, is the set of all subspaces of the vector space $\Fqn$. The projective space can be endowed with distance function $d_S(X,Y) = \dim(X) + \dim(Y) -…
We give an overview of various composite BPS configurations of string theory and M-theory p-branes represented as classical supergravity solutions. Type II string backgrounds can be obtained by S- and T- dualities from NS-NS string -…
The Plancherel decomposition of $L^2$ on a pseudo-Riemannian symmetric space $GL(n,C)/GL(n,R)$ has spectrum of $[n/2]$ types. We write explicitly orthogonal projectors separating spectrum into uniform pieces
For $d=4, 5, 6$, we exhibit the first examples of complete finite volume hyperbolic $d$-manifolds $M$ with cusps such that infinitely many $d$-orbifolds $M_{m}$ obtained from $M$ by generalized Dehn filling admit properly convex real…
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…
Non-trivial examples of generalized paracomplex structures (in the sense of the generalized geometry \`a la Hitchin) are constructed applying the twistor space construction scheme.
We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the…
Consider a $q$-ary block code satisfying the property that no $l$-letters long codeword's prefix occurs as a suffix of any codeword for $l$ inside some interval. We determine a general upper bound on the maximum size of these codes and a…
We construct positional numeral systems that work natively over nonderived polyadic $\left( m,n\right) $-rings whose addition takes $m$ arguments and multiplication takes $n$. In such rings, the length of an admissible additive word and a…
A $t$-fold packing of a projective space $\rm{PG}_n(q)$ is a collection $\mathcal{P}$ of line-spreads such that each line of $\rm{PG}_n(q)$ occurs in precisely $t$ spreads in $\mathcal{P}$. A $t$-fold packing $\mathcal{P}$ is transitive if…