How Many Zeroes?: Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity: 2 (CMS/CAIMS Books in Mathematics, 2) - Image 1

£46.37

Springer How Many Zeroes?: Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity: 2 (CMS/CAIMS Books in Mathematics, 2)

Name: How Many Zeroes?: Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity: 2 (CMS/CAIMS Books in Mathematics, 2)
Brand: Springer
Price: 46.37 GBP
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Geometry & Topology

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Description

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.

Product Specifications

Brand: Springer
Format: paperback
ASIN: 3030751767
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 07 November 2022
Listed Since: 12 October 2022

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Springer How Many Zeroes?: Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity: 2 (CMS/CAIMS Books in Mathematics, 2)

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