Related papers: Intersection lattices of cubic fourfolds

We give an explicit formula for the arithmetic intersection number of CM cycles on Lubin-Tate spaces for all levels. We prove our formula by formulating the intersection number on the infinite level. Our CM cycles are constructed by…

We study the geometry of a birational map between an intersection of a web of quadrics in seven-dimensional complex projective space that contains a plane and the double octic branched along the discriminant of the web.

In this paper we study special Fibonacci quaternions and special generalized Fibonacci-Lucas quaternions in quaternion algebras over finite fields.

Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…

We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…

Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.

Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogues: the multidimensional quadrilateral lattices, i.e. lattices x: Z^N -> R^M, whose…

We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…

We study the question of the existence of a decomposition of the diagonal for very general quartic and $(2,3)$-complete intersection $n$-folds. Using cycle-theoretic techniques of Lange, Pavic and Schreieder we reduce the question via a…

The quaternions form a 4-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tetranacci and Tetranacci-Lucas quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them.

We use computational linear algebra and commutative algebra to study spaces of relations satisfied by quadrilinear operations. The relations are analogues of associativity in the sense that they are quadratic (every term involves two…

Classification of noncommutative quadric hypersurfaces is one of the major projects in noncommutative algebraic geometry. In recent years, we are dedicated to complete the classification of noncommutative central conics. To achieve this…

We have found a "non-purely-constructive" method of acquiring algebraic cycles involving multiple steps. This note tries to present the main idea in the last step by concentrating on an example of 4-folds. The method demonstrates a contrast…

We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking…

We present a novel approach to the construction of new finite algebras and describe the congruence lattices of these algebras. Given a finite algebra $(B_0, \dots)$, let $B_1, B_2, \dots, B_K$ be sets that either intersect $B_0$ or…

We study the degree of the special cubic fourfolds in the Hilbert scheme of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signature (2, 20).

We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.

We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.

For every even number $n$, and every $n$-dimensional smooth hypersurface of $\mathbb{P}^{n+1}$ of degree $d$, we compute the periods of all its $\frac{n}{2}$-dimensional complete intersection algebraic cycles. Furthermore, we determine the…

We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…