کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4945983 | 1364076 | 2017 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the auto Igusa-zeta function of an algebraic curve
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study endomorphisms of complete Noetherian local rings in the context of motivic integration. Using the notion of an auto-arc space, we introduce the (reduced) auto-Igusa zeta series at a point, which appears to measure the degree to which a variety is not smooth that point. We conjecture a closed formula in the case of curves with one singular point, and we provide explicit formulas for this series in the case of the cusp and the node. Using the work of Denef and Loeser, one can show that this series will often be rational. These ideas were obtained through extensive calculations in Sage. Thus, we include a Sage script which was used in these calculations. It computes the affine arc spaces ânX provided that X is affine, n is a fat point, and the ground field is of characteristic zero. Finally, we show that the auto Poincaré series will often be rational as well and connect this to questions concerning new types of motivic integrals.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 79, Part 1, MarchâApril 2017, Pages 156-185
Journal: Journal of Symbolic Computation - Volume 79, Part 1, MarchâApril 2017, Pages 156-185
نویسندگان
Andrew R. Stout,