Tag Archives: projective varieties

Commutative Algebra 64

Posted on May 30, 2020 by limsup

Segre Embedding Throughout this article, k is a fixed algebraically closed field. We wish to construct the product in the category of quasi-projective varieties. For our first example, let be the projective variety defined by the homogeneous equation . We define … Continue reading →

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Commutative Algebra 62

Posted on May 25, 2020 by limsup

Irreducible Subsets of Projective Space Throughout this article, k is an algebraically closed field. We wish to consider irreducible closed subsets of . For that we need the following preliminary result. Lemma 1. Let be a graded ring; a proper homogeneous … Continue reading →

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Commutative Algebra 61

Posted on May 22, 2020 by limsup

In this article, we will consider algebraic geometry in the projective space. Throughout this article, k denotes an algebraically closed field. Projective Space Definition. Let . On the set , we consider the equivalence relation: The projective n-space is the set … Continue reading →

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