Related papers: Self-dual Harmonicity: the planar case
For an axiomatization of three-dimensional projective space based on points and planes, we discuss appropriate versions of the harmonicity axiom and the projectivity axiom, showing that each axiom is equivalent to its spatial dual.
Within an axiomatic framework for three-dimensional projective space based on lines alone, we explore the Fano axiom of harmonicity according to which the diagonal lines of a complete quadrilateral are not concurrent.
We take points and planes as fundamental, lines as derived, in an axiomatic formulation of three-dimensional projective space, the self-dual nature of which formulation renders automatic the principle of duality.
We investigate an `assumption of projectivity' that is appropriate to the self-dual axiomatic formulation of three-dimensional projective space.
We discuss homogeneity and universality issues in the theory of abstract linear spaces, namely, structures with points and lines satisfying natural axioms, as in Euclidean or projective geometry. We show that the two smallest projective…
Fano mechanism is the universal explanation of asymmetric resonance appearing in different systems. We report the evidence of Fano-like resonance in selective reflection from a resonant two-level medium. We draw an analogy with the…
We study projectively self-dual polygons and curves in the projective plane. Our results provide a partial answer to problem No 1994-17 in the book of Arnold's problems.
We prove divisorial canonicity of Fano double hypersurfaces of general position.
We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.
We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.
We prove that a general Fano hypersurface in a projective space over an algebraically closed field of arbitrary characteristic is separably rationally connected.
We consider mirror symmetry for Fano manifolds, and describe how one can recover the classification of 3-dimensional Fano manifolds from the study of their mirrors. We sketch a program to classify 4-dimensional Fano manifolds using these…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop harmonic conjugation in projective rectangles. We construct projective rectangles in some harmonic matroids (matroids where harmonic…
We calculate the Assouad dimension of a planar self-affine set $X$ satisfying the strong separation condition and the projection condition and show that $X$ is minimal for the conformal Assouad dimension. Furthermore, we see that such a…
As a continuation of a recent work of the same authors (arXiv:1504.07138), in this note we study the dimension theory of diagonally homogeneous triangular planar self-affine IFS.
Let $M$ be a smooth Fano threefold such that a canonical extension of the tangent bundle is an affine manifold. We show that $M$ is rational homogeneous.
As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this…
We investigate homological stability for the space of sections of Fano fibrations over curves in the context of weak approximation, and establish it for projective bundles, as well as for conic and quadric surface bundles over curves.
It is shown that the automorphism group of a binary $q$-analog of the Fano plane is either trivial or of order $2$.
It is shown how some results on harmonic maps within the chiral model can be carried over to self-dual gravity. The WZW-like action for self-dual gravity is found.