Characterizations of complex projective spaces and 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...

Biquaternions Lie Algebra and Complex-Projective Spaces

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Characterizations of Finite Projective and Affine Spaces

THEOREM 1. A finite incidence structure is isomorphic to the design of points and hyperplanes of a finite projective or affine space of dimension greater than or equal to 4 if and only if there are positive integers v, k, and y, with ju > 1 and (/A — l)(v — k) 7* (k — ju) such that the following assumptions hold. (I) Every block is on k points, and every two intersecting blocks are on p. common...

biquaternions lie algebra and complex-projective spaces

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

CHARACTERIZATIONS OF PROJECTIVE AND k-PROJECTIVE SEMIMODULES