Related papers: Gherardelli linkage and complete intersections

Let $\mathcal{H}$ be a set of given connected graphs. A graph $G$ is said to be $\mathcal{H}$-free if $G$ contains no $H$ as an induced subgraph for any $H\in \mathcal{H}$. The graph $G$ is super-edge-connected if each minimum edge-cut…

We consider links that are alternating on surfaces embedded in a compact 3-manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the polyhedral decomposition of alternating…

We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of the cuplength of the Lagrangian in various multiplicative generalised cohomology…

We prove the analogue of the Concordance Implies Isotopy in Codimension $\ge 3$ Theorem for link maps, together with some other its singular analogues. In the case of spherical link maps, a stronger result was independently obtained by P.…

The second Veronese ideal $I_n$ contains a natural complete intersection $J_n$ generated by the principal $2$-minors of a symmetric $(n\times n)$-matrix. We determine subintersections of the primary decomposition of $J_n$ where one…

This article describes a unirationality construction for general low degree complete intersections in projective space which is based on a variety of highly tangent lines. Applied to hypersurfaces, this implies that a general hypersurface…

We provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain pro-jective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete…

In this short note we show that Helly's Intersection Theorem holds for convex sets in uniquely geodesic spaces (in particular in CAT(0) spaces) without the assumption that the convex sets are open or closed.

We prove two conjectures on weighted complete intersections and give the complete classification of threefold weighted complete intersections in weighted projective space that are canonically or anticanonically embedded.

We discuss, on general grounds, how two subgraphs of a given Feynman graph can overlap with each other. For this, we use the notion of connecting and returning lines that describe how any subgraph is inserted within the original graph.…

We characterize the canonical algebras such that for all dimension vectors of homogeneous modules the corresponding module varieties are complete intersections (respectively, normal). We also investigate the sets of common zeros of…

A homemorphism between domains in $\mathbb R^n$, $n\ge 2$ is quasiconformal, with its intricate analytic and geometric consequences, if the (pointwise) linear dilatation -- a purely metric quantity -- is uniformly bounded. Gehring proved…

We prove a Lefschetz duality result for intersection homology. Usually, this result applies to pseudomanifolds with boundary which are assumed to have a "collared neighborhood of their boundary". Our duality does not need this assumption…

It is well known that for a subscheme $V$ in ${\mathbb P}^{n}$ of codimension two, the conditions (1) $V$ is ACM, and (2) $V$ is "licci" (i.e. $V$ is in the liaison class of a complete intersection) are equivalent. In higher codimension,…

Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space $(\mathbb{C}P^3, g_a)$, including nearly K\"ahler $\mathbb{C}P^3$. Notably, all extrinsically homogeneous hypersurfaces are…

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood and the in-neighbourhood of any vertex induce a semicomplete digraph. In this paper we study various…

Let $G$ and $H$ be disjoint embeddings of complete graphs $K_m$ and $K_n$ in $\mathbb{R}^3$ such that some cycle in $G$ links a cycle in $H$ with non-zero linking number. We say that $G$ and $H$ are *weakly linked* if the absolute value of…

We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by…

We show that the Voronoi conjecture is true for parallelohedra with simply connected $\delta$-surface. Namely, we show that if the boundary of parallelohedron $P$ remains simply connected after removing closed non-primitive faces of…

We use the "closed point sieve" to prove a variant of a Bertini theorem over finite fields. Specifically, given a smooth quasi-projective subscheme X of P^n of dimension m over F_q, and a closed subscheme Z in P^n such that Z intersect X is…