Related papers: Delta invariants of smooth cubic surfaces

The gauge invariant elastic metric on the shape space of surfaces involves the mean curvature and the normal deformation, i.e. the sum and the difference of the principal curvatures $\kappa_1,\kappa_2$. The proposed gauge invariant elastic…

For a cubic surface X, by considering the intermediate Jacobian J(Y) of the triple covering Y of the 3-dimensional projective space branching along X, Allcock, Carlson and Toledo constructed a period map per from the family of marked cubic…

The algebra of differential invariants under $SA_3(\mathbb{R})$ of generic parabolic surfaces $S^2 \subset \mathbb{R}^3$ with nonvanishing Pocchiola $4^{\text{th}}$ invariant $W$ is shown to be generated, through invariant differentiations,…

We consider the degree/diameter problem for graphs embedded in a surface, namely, given a surface $\Sigma$ and integers $\Delta$ and $k$, determine the maximum order $N(\Delta,k,\Sigma)$ of a graph embeddable in $\Sigma$ with maximum degree…

Recently Jeong and Kim [Phys. Rev. E {\bf 66}, 051605 (2002)] investigated the scaling properties of equilibrium self-flattening surfaces subject to a restricted curvature constraint. In one dimension (1D), they found numerically that the…

We prove that, if $\Gamma$ is a finite connected cubic vertex-transitive graph, then either there exists a semiregular automorphism of $\Gamma$ of order at least $6$, or the number of vertices of $\Gamma$ is bounded above by an absolute…

In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map of Weingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type…

We show that the circular chromatic index of a (sub)cubic graph with girth at least six is at most 7/2.

Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least $23$…

In this paper we show that a particular extrinsic pointwise hypersurface invariant is always non-positive on minimal hypersurfaces of constant curvature spaces and vanishes identically if and only if the hypersurface is rotational. We show…

Numerical Campedelli surfaces are minimal surfaces of general type with p_g=0 (and so q=0) and K^2=2. Although they have been studied by several authors, their complete classification is not known. In this paper we classify numerical…

We study the geometry of the moduli space of planes in a general cubic 5-fold and its deformation. We show that this moduli space is a smooth projective surface whose canonical bundle is ample. We also show that the variation of degree 1…

In this paper we give an upper bound on the number of rational points on an irreducible curve $C$ of degree $\delta$ defined over a finite field $\mathbb{F}_q$ lying on a Frobenius classical surface $S$ embedded in $\mathbb{P}^3$. This…

A quadratic invariant is defined as a quadratic form in the elements of a tensor that remains invariant under a group of coordinate transformations. It is proved that there are 7 quadratic invariants of the 21-element elastic modulus tensor…

We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…

Segre proved that a smooth cubic surface over Q is unirational iff it has a rational point. We prove that the result also holds for cubic hypersurfaces over any field, including finite fields.

We prove that the maximal number of conics in a smooth sextic $K3$-surface $X\subset\mathbb{P}^4$ is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible.

We prove that the strong chromatic index for each $k$-degenerate graph with maximum degree $\Delta$ is at most $(4k-2)\Delta-k(2k-1)+1$.

We give a combinatorial proof of a lattice point identity involving a lattice polygon and its dual, generalizing the formula $area(\Delta) + area(\Delta^*) = 6$ for reflexive $\Delta$. The identity is equivalent to the stringy Libgober-Wood…

We study the Seshadri constants of cyclic coverings of smooth surfaces. The existence of an automorphism on these surfaces can be used to produce Seshadri exceptional curves. We give a bound for multiple Seshadri constants on cyclic…