Related papers: Twenty-Seven Lines on a Cubic Surface and Heteroti…
It has been shown that 5-dimensional general relativity action extended by appropriate quadratic terms admits a singular superconducting cosmic string solution. We search for cosmic strings endowed with similar and extended physical…
A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R P^3$. The papers classifies the nonsingular curves cut in this way on non-singular cubic surfaces up to homeomorphism. Two issues new in the study related to the first…
The hexagonal tiling honeycomb is a beautiful structure in 3-dimensional hyperbolic space. It is called {6,3,3} because each hexagon has 6 edges, 3 hexagons meet at each vertex in a Euclidean plane tiled by regular hexagons, and 3 such…
The Kerr geometry is represented as being created by a source moving along an analytical complex world-line. The equivalence of this complex world-line and an Euclidean version of complex strings (hyperbolic strings) is discussed. It is…
The Hessian of a general cubic surface is a nodal quartic surface, hence its desingularisation is a K3 surface. We determine the transcendental lattice of the Hessian K3 surface for various cubic surfaces (with nodes and/or Eckardt points…
A geometrical correspondence between maximal surfaces in anti-De Sitter space-time and minimal surfaces in the Riemannian product of the hyperbolic plane and the real line is established. New examples of maximal surfaces in anti-De Sitter…
We show that semi-arithmetic surfaces of arithmetic dimension two which admit a modular embedding have exponential growth of mean multiplicities in their length spectrum. Prior to this work large mean multiplicities were rigorously…
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
The moduli space of cubic surfaces and its compactifications are classical and date back to the mid-nineteenth century. Recently, Schock described compactifications of moduli spaces of fully marked cubic surfaces with their 27 lines via…
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is…
We study relations in the Grothendieck ring of varieties which connect the Hilbert scheme of points on a cubic hypersurface $Y$ with a certain moduli space of twisted cubic curves on $Y$. These relations are generalizations of the…
We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as long range cubic or hexagonal order. Our proposed structures fill space with a combination of minimal surface patches…
We reconsider the issue of embedding space-time fermions into the four-dimensional N=2 world-sheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional…
The automorphism groups of the 27 lines on the smooth cubic surface or the 28 bitangents to the general quartic plane curve are well-known to be closely related to the Weyl groups of $E\_6$ and $E\_7$. We show how classical…
A theory in which points, lines, areas and volumes are on on the same footing is investigated. All those geometric objects form a 16-dimensional manifold, called C-space, which generalizes spacetime. In such higher dimensional space…
The most promising MSSM candidates of the heterotic string reveal some distinctive properties. These include gauge-top unification, a specific solution to the mu-problem and mirage pattern for the gaugino masses. The location of the top-…
Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and non-supersymmetric string vacua fills out a ``landscape'' whose features are largely unknown. It is then hoped that progress in…
Fractional superstrings are recently-proposed generalizations of the traditional superstrings and heterotic strings. They have critical spacetime dimensions which are less than ten, and in this paper we investigate model-building for the…
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integer coefficients. We establish a similar result for…
It is shown that there exist non-singular cubic surfaces in CP^3 containing 5 twistor lines. This is the maximum number of twistor fibres that a non-singular cubic can contain. Cubic surfaces in CP^3 with 5 twistor lines are classified up…