Related papers: Small complete caps from nodal cubics
We investigate the topological structures of Galois covers of surfaces of minimal degree (i.e., degree n) in n+1 dimensional complex projective space. We prove that for n is greater than or equal to 5, the Galois covers of any surfaces of…
We show that the perfect Euler brick (perfect cuboid) problem is equivalent to the following elementary question: do there exist coprime integers $a, b, m, n$ such that the two expressions $(2(a^2-b^2)mn)^2 + ((a^2+b^2)(m^2-n^2))^2$ and…
We consider the existence and construction of \textit{biclique covers} of graphs, consisting of coverings of their edge sets by complete bipartite graphs. The \textit{size} of such a cover is the sum of the sizes of the bicliques.…
We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical…
We show that geodesics in the upper half-plane attached to a maximal split torus or a real quadratic torus in $GL_{2, \mathbf{Q}}$ are the only irreducible algebraic curves whose image via the $j$-invariant is contained in an algebraic…
As was shown recently by P. Nurowski, to any rank 2 maximally nonholonomic vector distribution on a 5-dimensional manifold M one can assign the canonical conformal structure of signature (3,2). His construction is based on the properties of…
We study families of Galois covers of curves of positive genus. It is known that under a numerical condition these families yield Shimura subvarieties generically contained in the Jacobian locus. We prove that there are only 6 families…
This paper focuses on the embeddability of hypercubes in an important class of Cayley graphs, known as augmented cubes. An $n$-dimensional augmented cube $AQ_n$ is constructed by augmenting the $n$-dimensional hypercube $Q_n$ with…
We study the Galois descent of semi-affinoid non-archimedean analytic spaces. These are the non-archimedean analytic spaces which admit an affine special formal scheme as model over a complete discrete valuation ring, such as for example…
Fermi arcs represent the surface states at the boundary of a three-dimensional topological semimetal with the vacuum, illustrating the notion of bulk-boundary correspondence playing out in real materials. Their special character is tied up…
We prove that every odd semisimple reducible (2-dimensional) mod l Galois representation arises from a cuspidal eigenform. In addition, we investigate the possible different types (level, weight, character) of such a modular form. When the…
Genus two curves covering elliptic curves have been the object of study of many articles. For a fixed degree $n$ the subloci of the moduli space $\mathcal M_2$ of curves having a degree $n$ elliptic subcover has been computed for $n=3, 5$…
In this paper, we introduce \textit{splitting numbers} of subvarieties in a smooth variety for a Galois cover, and prove that the splitting numbers are invariant under certain homeomorphisms. By splitting numbers, we give a necessary and…
Using methods coming from non-formal equivariant quantization, we construct in this short note a unitary dual 2-cocycle on a discrete family of quotient groups of subgroups of the affine group of a local field (which is not of…
We show that the compactification of the moduli space of $n-$nodal curves of genus g, i.e. $\mathcal{N}_{g,n}:= \mathcal{M}_{g,2n} /G$, with $G:=(\mathbb{Z}_2)^n \rtimes S_n$, is of general type for $g \geq 24$, for all $n \in \mathbb{N}$.…
We classify 'primitive normal compactifications' of C^2 (i.e. normal analytic surfaces containing C^2 for which the curve at infinity is irreducible), compute the moduli space of these surfaces and their groups of auomorphisms. In…
We study marginal deformations of ${\cal N}=2$, $d=4$ long linear quiver CFTs using the holographic description. We find a two-parameter family of AdS$_5$ solutions that generically break all of supersymmetry, but preserve ${\cal N}=1$ for…
The Minimum Path Cover (MPC) problem consists of finding a minimum-cardinality set of node-disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on acyclic digraphs (DAGs) where, given a subset of…
An ordered biclique partition of the complete graph $K_n$ on $n$ vertices is a collection of bicliques (i.e., complete bipartite graphs) such that (i) every edge of $K_n$ is covered by at least one and at most two bicliques in the…
An approach for the computation of upper bounds on the size of large complete arcs is presented. We obtain in particular geometrical properties of irreducible envelopes associated to a second largest complete arc provided that the order of…