Related papers: On the classification of certain geproci sets
A recent paper showed how to find sets of finite affine or projective planes constructed on a common set of points, so that lines of one plane meet lines of a different plane in at most two points. In this paper, those results are…
We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…
We classify K3 surfaces with non-symplectic automorphism of order 16 in full generality. We show that the fixed locus contains only rational curves and points and we completely classify the seven possible configurations. If the…
Stacking, a potent ensemble learning method, leverages a meta-model to harness the strengths of multiple base models, thereby enhancing prediction accuracy. Traditional stacking techniques typically utilize established learning models, such…
We show that a complex planar curve homeomorphic to the projective line has at most four singular points. If it has exactly four then it has degree five and is unique up to a projective equivalence.
Recent work has applied supervised deep learning to derive continuous symmetry transformations that preserve the data labels and to obtain the corresponding algebras of symmetry generators. This letter introduces two improved algorithms…
We present two practical improvement techniques for unsupervised segmentation learning. These techniques address limitations in the resolution and accuracy of predicted segmentation maps of recent state-of-the-art methods. Firstly, we…
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
We investigate monodromy groups arising in enumerative geometry, with a particular focus on how these groups are influenced by prescribed symmetries. To study these phenomena effectively, we work in the framework of moduli stacks rather…
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…
We describe and study the loci equidistant from finitely many points in the so-called complex hyperbolic geometry, i.e., in the geometry of a holomorphic $2$-ball $\Bbb B$. In particular, we show that the bisectors (= the loci equidistant…
We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics. The three main types of problems we…
We exploit techniques from classical (real and complex) algebraic geometry for the study of the standard twistor fibration $\pi:\mathbb{CP}^{3}\to S^{4}$. We prove three results about the topology of the twistor discriminant locus of an…
Let $P$ be a set of $n$ points in the real plane contained in an algebraic curve $C$ of degree $d$. We prove that the number of distinct distances determined by $P$ is at least $c_d n^{4/3}$, unless $C$ contains a line or a circle. We also…
We consider the ring of invariants of n points on the projective line. The space (P^1)^n // PGL_2 is perhaps the first nontrivial example of a Geometry Invariant Theory quotient. The construction depends on the weighting of the n points.…
Bisectors are equidistant hypersurfaces between two points and are basic objects in a metric geometry. They play an important part in understanding the action of subgroups of isometries on a metric space. In many metric geometries…
We introduce a class of convex equivolume partitions. Expected $L_2-$discrepancy are discussed under these partitions. There are two main results. First, under this kind of partitions, we generate random point sets with smaller expected…
We prove the sharp bound of at most 64 lines on complex projective quartic surfaces (resp. affine quartics) that are not ruled by lines. We study configurations of lines on certain non-K3 surfaces of degree four and give various examples of…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
This paper applies techniques from algebraic and differential geometry to determine how to best pack points in real projective spaces. We present a computer-assisted proof of the optimality of a particular 6-packing in…