| 書(shū)目名稱(chēng) | How Many Zeroes? | | 副標(biāo)題 | Counting Solutions o | | 編輯 | Pinaki Mondal | | 視頻video | http://file.papertrans.cn/429/428655/428655.mp4 | | 概述 | First textbook containing complete proofs of various weighted versions of Bézout‘s theorem, Bernstein‘s theorem and its extension to the affine space.Gives a new proof of, and generalizes, Kushnirenko | | 叢書(shū)名稱(chēng) | CMS/CAIMS Books in Mathematics | | 圖書(shū)封面 |  | | 描述 | .This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein’s theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein’s original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko‘s results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students. . | | 出版日期 | Textbook 2021 | | 關(guān)鍵詞 | Number of solutions/zeros of systems of polynomials; affine Bezout problem; Bezout‘s theorem; Bernstein | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-75174-6 | | isbn_softcover | 978-3-030-75176-0 | | isbn_ebook | 978-3-030-75174-6Series ISSN 2730-650X Series E-ISSN 2730-6518 | | issn_series | 2730-650X | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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