Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
How Many Zeroes?: Counting Solutions of Systems of Polynomials Via Toric Geometry at Infinity

How Many Zeroes?: Counting Solutions of Systems of Polynomials Via Toric Geometry at Infinity

Mondal, Pinaki

Paperback

Series: Cms/Caims Books in Mathematics, Book 2

Geometry

ISBN10: 3030751767
ISBN13: 9783030751760
Publisher: Springer Nature
Published: Nov 7 2022
Pages: 352
Weight: 1.14
Height: 0.77 Width: 6.14 Depth: 9.21
Language: English

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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