相关论文: Lines, Quadrics, and Cremona Transformations in Tw…
We outline some features of higher dimensional models possessing a Quark-Lepton (QL) symmetry. The QL symmetric model in five dimensions is discussed, with particular emphasis on the use of split fermions. An interesting fermionic geography…
We call a set of points $Z\subset{\mathbb P}^{3}_{\mathbb C}$ an $(a,b)$-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point $P$ to a plane is a complete intersection of curves of degrees…
Let $\A$ be the incidence matrix of lines and points of the classical projective plane $PG(2,q)$ with $q$ odd. With respect to a conic in $PG(2,q)$, the matrix $\A$ is partitioned into 9 submatrices. The rank of each of these submatices…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled by a combination of two techniques, called minimisation and…
We study the modular representation theory of rank $3$ association schemes arising from partial geometries with parameters $(s,t,\alpha)$. First, we obtain an explicit closed formula for the Frame number of the point scheme in terms of the…
Three classes of classical r-matrices for sl(4,C) algebra are constructed in quasi-Frobenius algebra approach. They satisfy CYBE and are spanned respectively on 8,10,12 generators. The o(4,2) reality condition can be imposed only on the…
Convex polyominoes can be refined according to the number of direction changes in monotone paths connecting pairs of cells, leading to the notion of $k$-convexity. In particular, the cases $k=1$ and $k=2$ correspond to $L$-convex and…
The aim of this paper is to introduce a certain number of tools and results suitable for the study of valuations of higher rank on function fields of algebraic varieties. This will be based on a study of higher rank quasi-monomial…
A tautological system, introduced in \cite{LSY}\cite{LY}, arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a complex manifold $X$, equipped with…
We make a geometric study of the Geometric Rank of tensors recently introduced by Kopparty et al. Results include classification of tensors with degenerate geometric rank in $C^3\otimes C^3\otimes C^3$, classification of tensors with…
Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of…
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing:…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
We explain how the geometric framework introduced in arXiv:2508.11621 [math.AG] provides a universal property for the 2-rings of perfect complexes on qcqs spectral or Dirac spectral schemes. As an application, given a qcqs spectral or Dirac…
The defect of a curve over a finite field is the difference between the number of rational points on the curve and the Weil-Serre upper bound for the number of points on the curve. We present algorithms for constructing curves of genus 5,…
A solution is provided to the Bruxelles Problem, a geometric decision problem originally posed in 1825, that asks for a synthetic construction to determine when ten points in 3-space lie on a quadric surface, a surface given by the…
We study the rank-three lifting problem for incidence matrices of finite projective planes through residue-level determinant constraints invisible to tropical valuations alone. In residue characteristic $\neq 3$, any rank-$\le 3$ lift of…
This paper introduces advances in the geometry of the ratio of either two or three points in a line in the Desargues affine plane, and we see this as a ratio of elements of skew field which are constructed over a line in Desargues affine…
The purpose of this work is to close the local deformation problem of rank two Euclidean submanifolds in codimension two by describing their moduli space of deformations. In the process, we provide an explicit simple representation of these…