Related papers: Special effect varieties in higher dimension
We define a special type of hypersurface varieties inside $\mathbb{P}_k^{n-1}$ arising from connected planar graphs and then find their equivalence classes inside the Gr\"othendieck ring of projective varieties. Then we find a…
We apply Vojta's conjecture to blowups and deduce a number of deep statements regarding (generalized) greatest common divisors on varieties, in particular on projective space and on abelian varieties. Special cases of these statements…
Much recent attention has focused on theories with large extra compactified dimensions. However, while the phenomenological implications of the volume moduli associated with such compactifications are well understood, relatively little…
The split version of the Freudenthal-Tits magic square stems from Lie theory and constructs a Lie algebra starting from two split composition algebras [3, 17, 18]. The geometries appearing in the second row are Severi-Brauer varieties [20].…
We show that, for a polarised smooth projective variety $B \hookrightarrow \mathbb{P}^n_k$ of dimension $\geq 2$ over an infinite field $k$ and an abelian variety $A$ over the function field of $B$, there exists a dense Zariski open set of…
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…
We propose a framework to give a precise meaning to the intuitive notion of "family of real forms of a variety parametrised by a variety" and study some fundamental properties of this notion. As an illustration, for any $n \geq 1$, we…
Incidence varieties are spaces of $n$-tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varieties and realization moduli spaces associated to configurations…
A very large extra dimension may contain many localized branes. We discuss the possibility to formulate such models as a spin system where each spin indicates the supersymmetry direction preserved by the corresponding brane. In the…
The dimension of the space of SU(n) and translation invariant continuous valuations on $\mathbb{C}^n, n \geq 2$ is computed. For even $n$, this dimension equals $(n^2+3n+10)/2$; for odd $n$ it equals $(n^2+3n+6)/2$. An explicit geometric…
We prove that every projective variety of dimension n over a field of positive characteristic admits a morphism to projective n-space, etale away from the hyperplane H at infinity, which maps a chosen divisor into H and a chosen smooth…
In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…
This paper is devoted to the investigation of selected situations when the computation of projective (and other) equivalences of algebraic varieties can be efficiently solved with the help of finding projective equivalences of finite sets…
We prove that a smooth projective variety $X$ of dimension $n$ with strictly nef third, fourth or $(n-1)$-th exterior power of the tangent bundle is a Fano variety. Moreover, in the first two cases, we provide a classification for $X$ under…
A general formalism to investigate Bianchi type $VI_h$ universes is developed in an extended theory of gravity. A minimally coupled geometry and matter field is considered with a rescaled function of $f(R,T)$ substituted in place of the…
This monograph presents a detailed analysis of hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions. It continues with a detailed analysis of hypercomplex numbers in n…
We show that very general hypersurfaces in odd-dimensional simplicial projective toric varieties verifying a certain combinatorial property satisfy the Hodge conjecture (these include projective spaces). This gives a connection between the…
We classify all massive irreducible representations of super Poincar\'e in D=10. New Casimir operators of super Poincar\'e are presented whose eigenvalues completely specify the representation. It is shown that a scalar superfield contains…
Recently, Corvaja and Zannier obtained an extension of the Subspace Theorem with arbitrary homogeneous polynomials of arbitrary degreee instead of linear forms. Their result states that the set of solutions in P^n(K) (K number field) of the…
We show that the complex projective space has maximal degree (volume) among all n-dimensional Kahler-Einstein Fano manifolds admitting a holomorphic C^*-action with a finite number of fixed points. The toric version of this result,…