Related papers: Intersection lattices of cubic fourfolds

We study the number of planes for four dimensional projective hypersurfaces which has so-called inductive structure. We also determine transcendental lattices for cubic fourfolds of this type.

This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$--orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a…

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…

In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…

The coincidence site lattices (CSLs) of prominent 4-dimensional lattices are considered. CSLs in 3 dimensions have been used for decades to describe grain boundaries in crystals. Quasicrystals suggest to also look at CSLs in dimensions…

Cubical rectangles are being defined and explored here over the $n-$dimensional geometric cube $Q_n.$ They form a new class of geometric objects that includes all the edges and all the squares of the $n-$cube. We enumerate and characterize…

We consider the CSLs of 4-dimensional hypercubic lattices. In particular, we derive the coincidence index $\Sigma$ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given $\Sigma$. The hypercubic…

We compute the intersection multiplicities of special cycles in Lubin-Tate spaces, and formulate a new arithmetic fundamental lemma relating these intersections to derivatives of orbital integrals.

We study well-rounded ideal lattices from totally definite quaternion algebras. We prove existence and classification results, and illustrate our methods with examples.

We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.

We study the geometry, Hodge theory and derived category of cubic fourfolds containing several planes and their associated twisted K3 surfaces. We focus on the case of two planes intersecting along a line.

We calculate intersection forms of all 4-dimensional almost-flat manifolds

We develop an algorithm computing the transcendental lattice and the Mordell--Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces

It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour reduction of the fundamental transformation of quadrilateral…

We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in lines in the plane.

A systematic study of non-trivial cubic extensions of the four-dimensional Poincar\'e algebra is undertaken. Explicit examples are given with various techniques (Young tableau, characters etc).

The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…

Motivated by the fundamental results of the geometric algebra we study quadrilateral lattices in projective spaces over division rings. After giving the noncommutative discrete Darboux equations we discuss differences and similarities with…

We apply the specialization technique based on the decomposition of the diagonal to find an explicit example over $\mathbb{Q}$ of a quadric and cubic hypersurface in $\mathbb{P}^6$ such that their intersection is a smooth stably irrational…

Chasles' Quadrilateral Theorem is a classical statement about four tangents to a conic that simultaneously circumscribe a circle. In its various formulations, it relates the concurrence of certain lines to the existence of confocal conics…