Related papers: A Generalization of Desargues' Involution Theorem
We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal,…
We use the fact that a projective half-spin representation of $Spin_{12}$ has an open orbit to generalize Pfister's result on quadratic forms of dimension 12 in $I^3$ to orthogonal involutions.
As a natural application of the {\it theory of geometric averaging} in Finsler geometry and generalized Finsler geometry, a new approach to investigate {\it generalized Finsler geometry}, based on a convex invariance of the average…
We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.
We prove the invariance of plurigenera under smooth projective deformations in full generality. The proof is done by several estimates of singular hermitian metrics in terms of $L^{2}$-extension theorem of holomorphic sections.
This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…
This Note presents the resolution of a differential system on the plane that translates a geometrical problem about isotropic deformations of area and length. The system stems from a probability study on deformed random fields [J.Fournier…
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
We present a generalization of Descartes' theorem for the family of polytopal sphere packings arising from uniform polytopes. The corresponding quadratic equation is expressed in terms of geometric invariants of uniform polytopes which are…
In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open…
I present a simple derivation of the de Gennes narrowing phenomenon.
We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.
The Mullineux involution is an important map on $p$-regular partitions that originates from the modular representation theory of $\mathcal{S}_n$. In this paper we study the Mullineux transpose map and the generalized column regularization…
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
This is an expository paper which explores the ideas of the authors' paper "From Affine Geometry to Complex Geometry", arXiv:0709.2290. We explain the basic ideas of the latter paper by going through a large number of concrete, increasingly…
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
We study the evolution equations for a regularized version of Dirac-geodesics, which are the one-dimensional version of Dirac-harmonic maps. We show that for the regularization being sufficiently large, the evolution equations subconverge…