Related papers: Algebraic interaction strength for translation sur…
Currently, solid interfaces composed of two-dimensional materials (2D) in contact with metal surfaces (m-surf) have been the subject of intense research, where the borophene bilayer (BBL) has been considered a prominent material for the…
We show that $m$ points and $n$ two-dimensional algebraic surfaces in $\mathbb{R}^4$ can have at most $O(m^{\frac{k}{2k-1}}n^{\frac{2k-2}{2k-1}}+m+n)$ incidences, provided that the algebraic surfaces behave like pseudoflats with $k$ degrees…
We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex…
This memoir is devoted to the study of formal-analytic arithmetic surfaces. These are arithmetic counterparts, in the context of Arakelov geometry, of germs of smooth complex-analytic surfaces along a projective complex curve.…
The aim of this survey is to explore complete intersection monomial curves from a contemporary perspective. The main goal is to help readers understand the intricate connections within the field and its potential applications. The…
We present a computational method for detecting highly singular members in families of algebraic varieties. Applying this approach to a family of numerical Godeaux surfaces, we obtain explicit examples with many singularities. In…
We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…
In this paper, we provide two different resolutions of structural sheaves of projectivized tangent bundles of smooth complete intersections. These resolutions allow in particular to obtain convenient (and completely explicit) descriptions…
We introduce a twisted cohomology cocycle over the Teichmueller flow and prove a "spectral gap" for its Lyapunov spectrum with respect to the Masur-Veech measures. We then derive Hoelder estimates on spectral measures and bounds on the…
To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface. They have prominently featured in many interesting constructions in algebraic…
We consider random topologies of surfaces generated by cubic interactions. Such surfaces arise in various contexts in 2-dimensional quantum gravity and as world-sheets in string theory. Our results are most conveniently expressed in terms…
A translational surface is a tensor product surface constructed from two space curves by translating one along the other. These surfaces are common within geometric modeling and, since their description is parametric, it is desirable to…
We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. Especially, we obtain effective density theorems on $\mathcal{H}(2)$ for orbits of the upper triangular subgroup $P$ of…
The height of a toric variety and that of its hypersurfaces can be expressed in convex-analytic terms as an adelic sum of mixed integrals of their roof functions and duals of their Ronkin functions. Here we extend these results to the…
We give the values of the Siegel-Veech constants associated with saddle connections having distinct endpoints on translation surfaces in Prym eigenform loci in $\Omega \mathcal{M}_3(2,2)^{\rm odd}$. In particular, we show that these…
A new approach is proposed for study structure and properties of the total squared mean curvature $W$ of surfaces in ${\bf R}^3$. It is based on the generalized Weierstrass formulae for inducing surfaces. The quantity $W$ (Willmore…
We consider the Kepler problem on surfaces of revolution that are homeomorphic to $S^2$ and have constant Gaussian curvature. We show that the system is maximally superintegrable, finding constants of motion that generalize the Runge-Lentz…
This thesis deals with automorphisms of real algebraic surfaces, which are polynomial transformations with a polynomial inverse. The main concern is whether their restriction to the real locus reflects all the richness of the complex…
The intersection of two orthogonal cylinders represents a classical problem in computational geometry with direct applications to engineering design, manufacturing, and numerical simulation. While analytical solutions exist for the fully…
We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson…