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How many zeroes? = counting solution...

Mondal, Pinaki.

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How many zeroes? = counting solutions of systems of polynomials via toric geometry at infinity /

Record Type:	Electronic resources : Monograph/item
Title/Author:	How many zeroes?/ by Pinaki Mondal.
Reminder of title:	counting solutions of systems of polynomials via toric geometry at infinity /
Author:	Mondal, Pinaki.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xv, 352 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Toric varieties. -
Online resource:	https://doi.org/10.1007/978-3-030-75174-6
ISBN:	9783030751746

How many zeroes? = counting solutions of systems of polynomials via toric geometry at infinity /
Mondal, Pinaki.

How many zeroes?counting solutions of systems of polynomials via toric geometry at infinity /[electronic resource] :by Pinaki Mondal. - Cham :Springer International Publishing :2021. - xv, 352 p. :ill. (some col.), digital ;24 cm. - CMS/CAIMS books in mathematics,v. 22730-6518 ;. - Cms/caims books in mathematics ;v. 2..

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 K. 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 a second-year graduate students.

ISBN: 9783030751746

Standard No.: 10.1007/978-3-030-75174-6doiSubjects--Topical Terms:

699748
Toric varieties.

LC Class. No.: QA564 / .M65 2021

Dewey Class. No.: 516.35

How many zeroes? = counting solutions of systems of polynomials via toric geometry at infinity /
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245 1 0 $a How many zeroes? $h [electronic resource] : $b counting solutions of systems of polynomials via toric geometry at infinity / $c by Pinaki Mondal.
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300 $a xv, 352 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a CMS/CAIMS books in mathematics, $x 2730-6518 ; $v v. 2
520 $a 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 K. 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 a second-year graduate students.
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