Two Conjectures of Victor Thébault Linking Tetrahedra with Quadrics
نویسنده
چکیده
We prove two of Thébault’s conjectures. The first (1949) links four lines, that they are rulings of hyperbolic paraboloids or that they are coplanar, with orthocentric or isodynamic tetrahedra, respectively. The second (1953) links the radical center of four spheres with elements of tetrahedra.
منابع مشابه
Gorenstein Algebras Presented by Quadrics
We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a number of different techniques, including liaison theory and generic initial ideals.
متن کاملOn the Invertibility of Motives of Affine Quadrics
We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives DM(k,Z[1/e]) (where k is a perfect field of exponential characteristic e). We also establish a motivic version of the conjectures of Po Hu on products of certain affine Pfister quadrics. Both of these results are obtained by studying a novel conservative functor on (a su...
متن کاملHigh Rank Linear Syzygies on Low Rank Quadrics
We study the linear syzygies of a homogeneous ideal I ⊆ S = Symk(V ), focussing on the graded betti numbers bi,i+1 = dimk Tori(S/I, k)i+1. For a variety X and divisor D with V = H(D), what conditions on D ensure that bi,i+1 6= 0? In [2], Eisenbud shows that a decomposition D∼A+B such that A and B have at least two sections gives rise to determinantal equations (and corresponding syzygies) in IX...
متن کامل2 00 6 Codes defined by forms of degree 2 on quadric and non - degenerate hermitian varieties in P 4
We study the functional codes of second order defined by G. Lachaud on X ⊂ P(Fq) a quadric of rank(X )=3,4,5 or a non-degenerate hermitian variety. We give some bounds for the number of points of quadratic sections of X , which are the best possible and show that codes defined on non-degenerate quadrics are better than those defined on degenerate quadrics. We also show the geometric structure o...
متن کاملEstimating the Parameters for Linking Unstandardized References with the Matrix Comparator
This paper discusses recent research on methods for estimating configuration parameters for the Matrix Comparator used for linking unstandardized or heterogeneously standardized references. The matrix comparator computes the aggregate similarity between the tokens (words) in a pair of references. The two most critical parameters for the matrix comparator for obtaining the best linking results a...
متن کامل