How Many Zeroes? : Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity Hardback
by Pinaki Mondal
Part of the CMS/CAIMS Books in Mathematics series
Hardback
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.
Information
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Only a few left - usually despatched within 24 hours
- Format:Hardback
- Pages:352 pages, 81 Illustrations, color; 7 Illustrations, black and white; XV, 352 p. 88 illus., 81 illus
- Publisher:Springer Nature Switzerland AG
- Publication Date:07/11/2021
- Category:
- ISBN:9783030751739
Other Formats
- Paperback / softback from £49.15
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£49.15
Information
-
Only a few left - usually despatched within 24 hours
- Format:Hardback
- Pages:352 pages, 81 Illustrations, color; 7 Illustrations, black and white; XV, 352 p. 88 illus., 81 illus
- Publisher:Springer Nature Switzerland AG
- Publication Date:07/11/2021
- Category:
- ISBN:9783030751739
