The projective geometry arising from a hollow module

Some Extremal Contractions between Smooth Varieties Arising from Projective Geometry

Let ψ : X → Y be a proper morphism with connected fibers from a smooth projective variety X onto a normal variety Y , i.e. a contraction. If −KX is ψ-ample, then ψ is said to be an extremal contraction and if moreover Pic(X)/ψ(Pic(Y )) ≃ Z then ψ is said to be an elementary extremal contraction or a Fano-Mori contraction. Usually contractions are divided into two types: birational and of fiber ...

Torsors and Ternary Moufang Loops Arising in Projective Geometry

Abstract. We give an interpretation of the construction of torsors from [BeKi10a] in terms of classical projective geometry. For the Desarguesian case, this leads to a reformulation of certain results from [BeKi10a], whereas for the Moufang case the result is new. But even in the Desarguesian case it sheds new light on the relation between the lattice structure and the algebraic structures of a...

Evaluation Codes Arising from some Subsets of the Projective Space

In this paper we work with some evaluation codes arising from a specific subset of the projective space. We compute the a−invariant of the corresponding coordinate ring and the main parameters of these codes: length, dimension and minimum distance. We obtain that these codes are MDS codes. Mathematics Subject Classification: 94B27, 94B60

Projective geometry - from foundations to applications

Applications of Some Properties of the Canonical Module in Computational Projective Algebraic Geometry

Introduction. The aim of this article is to show how one may use interesting properties of the canonical module for computational applications. It seems that the ideas we develop here are not used in computational algebraic geometry today. We do not claim any major improvement on the theoretical complexity of the problems we address, however we have the feeling that this alternative approach fo...