کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778520 | 1633774 | 2017 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Finiteness theorems on hypersurfaces in partial differential-algebraic geometry
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
Hrushovski's generalization and application of Jouanolou (1978) [9] is here refined and extended to the partial differential setting with possibly nonconstant coefficient fields. In particular, it is shown that if X is a differential-algebraic variety over a partial differential field F that is finitely generated over its constant field F0, then there exists a dominant differential-rational map from X to the constant points of an algebraic variety V over F0, such that all but finitely many codimension one subvarieties of X over F arise as pull-backs of algebraic subvarieties of V over F0. As an application, it is shown that the algebraic solutions to a first order algebraic differential equation over C(t) are of bounded height, answering a question of Eremenko. Two expected model-theoretic applications to DCF0,m are also given: 1) Lascar rank and Morley rank agree in dimension two, and 2) dimension one strongly minimal sets orthogonal to the constants are âµ0-categorical. A detailed exposition of Hrushovski's original (unpublished) theorem is included, influenced by Ghys (2000) [5].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 314, 9 July 2017, Pages 726-755
Journal: Advances in Mathematics - Volume 314, 9 July 2017, Pages 726-755
نویسندگان
James Freitag, Rahim Moosa,