How Many Zeroes?

How Many Zeroes?
Author :
Publisher : Springer Nature
Total Pages : 358
Release :
ISBN-10 : 9783030751746
ISBN-13 : 3030751740
Rating : 4/5 (740 Downloads)

Book Synopsis How Many Zeroes? by : Pinaki Mondal

Download or read book How Many Zeroes? written by Pinaki Mondal and published by Springer Nature. This book was released on 2021-11-07 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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