Related papers: Miquel point and isogonal conjugation
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
In this paper, we characterise ovoidal cones by their intersection numbers. We first show that a set of points of $\mathrm{PG}(4,q)$ which intersects planes in $1$, $q+1$ or $2q+1$ points is either an ovoidal cone or a parabolic quadric,…
We prove that the moduli stacks of marked and labelled Hodge-special Gushel-Mukai fourfolds are isomorphic. As an application, we construct rational maps from the stack of Hodge-special Gushel-Mukai fourfolds of discriminant $d$ to the…
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad\'e table. We give some properties of…
We determine the action of the product of symmetric groups on the cohomology of certain moduli of weighted pointed rational curves. The moduli spaces that we study are of stable rational curves with m+n marked points where the first m…
It is known that some GIT compactifications associated to moduli spaces of either points in the projective line or cubic surfaces are isomorphic to Baily-Borel compactifications of appropriate ball quotients. In this paper, we show that…
Let $\{P_1, P_2, P_3, P_4\}$ be a quadruplet of points in $S^3$ . We define a ``dual'' quadruplet of it in a conformal geometric way. We show that the dual of a dual quadruplet coincides with the original one. We also show that the cross…
We study the homology of pointed sets over a partially commutative monoid.
Both the USA TST 2008 and the ELMO Shortlist 2013 suggested two issues that are connected to fixed points. These problems provide a strong linkage between the various attributes of specific points in a triangle. In this article, we will…
We introduce Macdonald polynomials indexed by $n$-tuples of partitions and characterized by certain orthogonality and triangularity relations. We prove that they can be explicitly given as products of ordinary Macdonald polynomials…
It is well established that a general pair of twisted cubic curves in complex projective space has ten common secant lines. As an initial investigation, we show that the monodromy group of the ten common secant lines over the complex…
We prove that if a simplicial complex is shellable, then the intersection lattice for the corresponding diagonal arrangement is homotopy equivalent to a wedge of spheres. Furthermore, we describe precisely the spheres in the wedge, based on…
We formalize a ten-face triangular wing set on a regular icosahedron under a vertex labeling N, S, U1-U5, L1-L5 with rotation axis NS. The wing faces satisfy: (i) each face is an isosceles 36-36-108 triangle with a 36-degree angle anchored…
In this paper, we study the geometry of trisections on certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in order to construct trisections and related plane curves with interesting properties…
We give a general construction of triangulations starting from a walk in the quarter plane with small steps, which is a discrete version of the mating of trees. We use a special instance of this construction to give a bijection between maps…
In this paper, a theorem about similar triangles is proved. It shows that two small and four large triangles similar to the original triangle can appear if we choose well among several intersections of the perpendicular bisectors of the…
A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions…
Let $F$ be Cayley's ruled cubic surface in a projective three-space over any commutative field $K$. We determine all collineations fixing $F$, as a set, and all cubic forms defining $F$. For both problems the cases $|K|=2,3$ turn out to be…
We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several equivalent conditions for the OPUC to be mirror symmetric…
Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known…