Order 1 strongly minimal sets in differentially closed fields

Eric Rosen

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Order 1 strongly minimal sets in differentially closed fields

Eric Rosen

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Abstract

We give a classification of non-orthogonality classes of trivial order 1 strongly minimal sets in differentially closed fields. A central idea is the introduction of $τ$-forms, functions on the prolongation of a variety which are analogous to 1-forms. Order 1 strongly minimal sets then correspond to smooth projective curves with $τ$-forms. We also introduce $τ$-differentials, algebraic versions of $τ$-forms which are analogous to usual differentials, and develop their basic properties. This enables us to reformulate our classification scheme-theoretically in terms of curves with $τ$-invertible sheaves. This work partially generalizes and extends results of Hrushovski and Itai.

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BibTeX RIS

Eric Rosen. 2007-01-19. Order 1 strongly minimal sets in differentially closed fields. https://arxiv.org/abs/math/0510233

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