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How Many Zeroes?
- Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity
Engelsk Paperback
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How Many Zeroes?
- Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity
Engelsk Paperback

573 kr
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Om denne bog

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 detaljer
Sprog:
Engelsk
Sider:
352
ISBN-13:
9783030751760
Indbinding:
Paperback
Udgave:
ISBN-10:
3030751767
Udg. Dato:
7 nov 2022
Længde:
0mm
Bredde:
155mm
Højde:
235mm
Forlag:
Springer Nature Switzerland AG
Oplagsdato:
7 nov 2022
Forfatter(e):
Kategori sammenhænge