A remarkable result of [Segre43] says that a smooth cubic surface over Q is unirational iff it has a rational point. [Manin72, II.2] observed that similar arguments work for higher dimensional cubic hypersurfaces satisfying a certain genericity assumption over any infinite field. [CT-S-SD87, 2.3.1] extended the result of Segre to any normal cubic hypersurface (other than cones) over a field of ...

Abstract. Table of contents : §1. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1. §2. Conjugation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. §3. Reflection mapping R′ h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Given a homogeneous ideal in polynomial ring over $\Bbb{C}$, we adapt the construction of Newton-Okounkov bodies to obtain convex subset Euclidean space such that suitable integral this set computes {\it Segre zeta function\/} ideal. That is, extract numerical information class subscheme projective from an associated (unbounded) set. The result generalizes arbitrary subschemes form previously k...

We show that biholomorphic automorphisms of a real analytic hypersurface in I C can be considered as (pointwise) Lie symmetries of a holomorphic completely overdetermined involutive second order PDE system defining its Segre family. Using the classical S.Lie method we obtain a complete description of infinitesimal symmetries of such a system and give a new proof of some well known results of CR...

In [1, 4], Fulton defines the notion of the Segre class s(X, Y) ∈ A∗X of a closed embedding of schemes X→ Y over a field k. As in Fulton, all of our schemes are finite type over a ground field k which may be of arbitrary characteristic unless stated otherwise. The Segre class allows us to measure the way in which X sits inside Y, and is functorial for sufficiently nice maps ([1, 4.2]). One impo...