Related papers: A Generalization of Desargues' Involution Theorem
This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
Based on the classical Pl\"ucker correspondence, we present algebraic and geometric properties of discrete integrable line complexes in $CP^3$. Algebraically, these are encoded in a discrete integrable system which appears in various guises…
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
We give a revision of the proof of a Mazur-Ulam theorem for generalized gyrovector spaces given in the paper "Generalized gyrovector spaces and a Mazur-Ulam theorem" published in Publ. Math. Debrecen, 87 (2015), 393--413.
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.
We give the converse to Dirichlet's theorem on primes in arithmetic progressions by generalizing an old result of Guinand.
Arvanitakis established recently a theorem which is a common generalization of Michael's convex selection theorem and Dugundji's extension theorem. In this note we provide a short proof of a more general version of Arvanitakis' result.
We discuss various phenomena of tangency in projective and convex geometry.
A classical theorem of Riemannian geometry, due in its original form to Cartan, states that the Taylor expansion of the metric in geodesic normal coordinates is a universal formal power series involving only the symmetrizations of the…
General invariants of a geometric mapping of a symmetric affine connection space are obtained in this paper. These invariants are generalizations of the previous obtained basic invariants (see [16]). Moreover, these invariants are related…
We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many…
We exhibit examples of projective varieties with degenerate Gauss mappings and determine numerical invariants of such varieties. Our examples provide counter-examples to an asserted structure theorem of Griffiths and Harris (Ann. Sci. ENS…
In this chapter we briefly review the basics of the theory of stellar evolution.
We give a fully algebraic proof of an important theorem of Demailly, stating the existence of many Green-Griffiths jet differentials on a complex projective manifold of general type. To this end, we introduce a new algebraic version of the…
We give an interpretation of the construction of torsors from preceding work (Bertram, Kinyon: Associative Geometries. I, J. Lie Theory 20) in terms of classical projective geometry. For the Desarguesian case, this leads to a reformulation…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.
In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.
A sequence of generalizations of Cartan's conservation of torsion theorem is given for n-dimensional differentiable manifolds having a general linear connection.