When n satisfies an inequality which is almost best possible, we prove that the k-plane sections of every smooth, degree d, complex hypersurface in Pn dominate the moduli space of degree d hypersurfaces in Pk. As a corollary we prove that, for n sufficiently large, every smooth, degree d hypersurface in Pn satisfies a version of “rational simple connectedness”. 1. Statement of results In their ...

This note is an extension of the paper [HMP]. The main theorem of [HMP] states that a relatively smooth hypersurface (i.e. a hypersurface whose singular locus has sufficient large codimension with respect to its degree) is unirational. A mild modification can generalize this to complete intersections. As an application, we will show the Fano variety of a relatively smooth hypersurface is also u...

In our previous work (2002), we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse; in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semiRiemannian Banach space is an essen...

A hypersurface of order (n+ 1)(ph − 1) in projective space of dimension n of prime characteristic p has an invariant monomial. This implies that a hypersurface of order (n+1)(ph−1)−1 determines an invariant point. A hypersurface of order d < n+ 1 in a projective space of dimension n of characteristic two has an invariant set of subspaces of dimension d− 1 determined by one linear condition on t...

In this article, we prove that there exists at least one chord orbit of Hamilton vector field connecting the Legendre submanifold on a given energy stable hypersurface in some symplectic manifolds. Démonstration de existence de chord orbital de hamiltonien en une stable hypersurface dans une variété symplectique. Résumé. Soit Σ une hypersurface close en variété symplectique, Il est de montrer q...

We show that, in relativistic field theories, the thermal correlation function of N bosonic operators at sufficiently spacelike-separated points shows exponentially weak dependence on time variables t_1,...,t_N, when space separations are held fixed. For classical theory, vanishes all spacelike separated

Helfer in [6] was the first to produce an example of a spacelike Lorentzian geodesic with a continuum of conjugate points. In this paper we show the following result: given an interval [a, b] of IR and any closed subset F of IR contained in ]a, b], then there exists a Lorentzian manifold (M, g) and a spacelike geodesic γ : [a, b] → M such that γ(t) is conjugate to γ(a) along γ iff t ∈ F .

We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an “elliptic end” (resp. a “hyperbolic end”) if the monodromy matrix at the end is diagonalizable with eigenvalues in the unit circle (resp. in the reals). A...