Inductive characterizations of hyperquadrics

Cohomological Characterizations of Projective Spaces and Hyperquadrics

Projective spaces and hyperquadrics are the simplest projective algebraic varieties, and they can be characterized in many ways. The aim of this paper is to provide a new characterization of them in terms of positivity properties of the tangent bundle (Theorem 1.1). The first result in this direction was Mori’s proof of the Hartshorne conjecture in [Mor79] (see also Siu and Yau [SY80]), that ch...

Inductive Characterizations of Finite Interval Orders and Semiorders

We introduce an inductive definition for two classes of orders. By simple proofs, we show that one corresponds to the interval orders class and that the other is exactly the semiorders class. To conclude we consider most of the known equivalence theorems on interval orders and on semiorders, and we give simple and direct inductive proofs of these equivalences with ours characterizations.

Umbilic Points and Real Hyperquadrics

There exist polynomial identities asociated to normal form, which yield an existence and uniqueness theorem. The space of normalized real hypersurfaces has a natural group action. Umbilic point is defined via normal form. A nondegenerate analytic real hypersurface is locally biholomorphic to a real hyperquadric if and only if every point of the real hypersurface is umbilic. 0. Introduction An a...

Congruence and Similarity Classification of Real Hyperquadrics

We shall begin by recalling some material from quadrics1.pdf, which gave the classification of hyperquadrics in R and C up to affine equivalence: CONGRUENCE OR ISOMETRY CLASSIFICATION PROBLEM. Given two affine hyperquadrics Σ1 and Σ2 in R , is there a congruence or isometry T from R to itself mapping Σ1 onto Σ2? There are two possible versions of the question. An arbitrary isometry T from R to ...

General characterizations of inductive inference over arbitrary sets of data presentations