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Chains of Differential Subvarieties in an Algebraic Variety

✍ Scribed by Wai Yan Pong

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
108 KB
Volume
248
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let X be a δ-variety over some δ-field . Denote by td δ X/ , or simply td δ X if the ground field is understood, the δ-transcendental degree of X over . Suppose td δ X = d; Johnson [Comment. Math. Helv. 44 (1969), 207-216] showed that there is an increasing chain of δ-subvarieties of length ωd in X. The question, also known as the Kolchin Catenary Problem, is: Given a point x ∈ X, is there an increasing chain of δ-subvarieties of length ωd starting at x? We will give an affirmative answer to this question if X is an algebraic variety.

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