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Explore the intricate world of polynomial equations with “How Many Zeroes?: Counting Solutions of Systems of Polynomials Via Toric Geometry at Infinity.” This graduate-level textbook offers a unique perspective on estimating isolated solutions using the powerful framework of toric geometry. Delve into Bernstein’s theorem, a cornerstone of counting solutions of generic systems, and its extensions to affine space. The book meticulously synthesizes research, providing complete proofs and practical applications. Discover how these techniques generalize Kushnirenko’s results on Milnor numbers, offering insights that predated modern toric geometry. Written for second-year graduate students, this accessible overview equips readers with the necessary algebraic geometry tools for a comprehensive understanding. Perfect for mathematicians and researchers seeking to deepen their knowledge of computational algebraic geometry and its foundational theorems.
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