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How Many Zeroes Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity 1st Edition by Pinaki Mondal ISBN 9783030751746 3030751740

Name: How Many Zeroes Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity 1st Edition by Pinaki Mondal ISBN 9783030751746 3030751740
SKU: EB-36143328
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How Many Zeroes Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity 1st Edition Pinaki Mondal Digital Instant Download

Author(s): Pinaki Mondal

ISBN(s): 9783030751746, 9783030751739, 3030751732, 3030751740

Edition: 1

File Details: PDF, 9.09 MB

Year: 2021

Language: English

SKU: EB-36143328 Category: Mathematics - Geometry and Topology Tag: Pinaki Mondal

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How Many Zeroes Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity 1st Edition by Pinaki Mondal – Ebook PDF Instant Download/Delivery: 9783030751746 ,3030751740
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Product details:

ISBN 10: 3030751740
ISBN 13: 9783030751746
Author: Pinaki Mondal

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.

How Many Zeroes Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity 1st Edition Table of contents:

1. Introduction

2. A brief history of points at infinity in geometry

Part I. Preliminaries

3. Quasiprojective varieties over algebraically closed fields

4. Intersection multiplicity

5. Convex polyhedra

Part II. Number of Zeroes on the Torus

6. Toric varieties over algebraically closed fields

7. Number of zeroes on the torus: BKK bound

Part III. Beyond the Torus

8. Number of zeroes on the affine space I: (Weighted) Bézout theorems

9. Intersection multiplicity at the origin

10. Number of zeroes on the affine space II: the general case

11. Milnor number of a hypersurface at the origin

12. Beyond this book

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