相关论文: Lines on Del Pezzo surfaces and transfinite hetero…

We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…

Mysterious duality is a relationship, described by Vafa in 2000, between $\frac12$-BPS branes in Type II supergravity in dimension $D=d+2$ and rational curves on del Pezzo surfaces of degree $d$. We show that both sides of this…

We study the slippage on hierarchical fractal superhydrophobic surfaces, and find an unexpected rich behavior for hydrodynamic friction on these surfaces. We develop a scaling law approach for the effective slip length, which is validated…

In an algebro-geometric way, we completely determine whether smooth del Pezzo surfaces are K-(semi)stable or not.

Fractal behavior and long-range dependence have been observed in tele-traffic measurement and characterization. In this paper we show results of application of the fractal analysis to internet traffic via various methods. Our result…

We discuss the geometry of timelike surfaces (two-dimensional submanifolds) in a Lorentzian manifold and its interpretation in terms of general relativity. A classification of such surfaces is presented which distinguishes four cases of…

We develop a strategy to classify the components of the space of sections of a del Pezzo fibration over $\mathbb{P}^{1}$. In particular, we prove the Movable Bend and Break lemma for del Pezzo fibrations. Our approach is motivated by…

The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend…

We propose a nonperturbative definition of heterotic string theory on arbitrary multidimensional tori.

We consider the three-dimensional Ising model slightly below its critical temperature, with boundary conditions leading to the presence of an interface. We show how the interfacial properties can be deduced starting from the particle modes…

The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal…

We study orbifold compactifications of heterotic strings on Enriques surfaces. We classify the inequivalent shift vectors for both the E8\times E8 and Spin(32)/Z2 lattices, and analyse the light spectrum of the resulting models. We show…

We briefly review the equations of motion and the space-time interval due to the nonlinear cosmic string that have been derived in ref. [3] for the first time. The different types of isotropic and nonisotropic geodesic lines in the…

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…

There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…

In his book "Cubic forms" Manin discovered that del Pezzo surfaces are related to root systems. To explain the many numerical coincidences Batyrev conjectured that a universal torsor on a del Pezzo surface can be embedded in a certain…

We introduce a class of noncommutative surfaces called Artin--Schelter surfaces of del Pezzo types, which contains del Pezzo surfaces as special cases. We show that the moduli stacks of marked Artin--Schelter surfaces of del Pezzo types are…

Given a geometrically irreducible subscheme X in P^n over F_q of dimension at least 2, we prove that the fraction of degree d hypersurfaces H such that the intersection of H and X is geometrically irreducible tends to 1 as d tends to…

In this paper, we consider the following problem: Does there exist a cubic surface over $\mathbb{Q}$ which contains no line over $\mathbb{Q}$, yet contains a line over every completion of $\mathbb{Q}$? This question may be interpreted as…

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously…