How Many Zeroes?
Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity
Series: CMS/CAIMS Books in Mathematics; 2;
- Publisher's listprice EUR 64.19
-
27 229 Ft (25 932 Ft + 5% VAT)
The price is estimated because at the time of ordering we do not know what conversion rates will apply to HUF / product currency when the book arrives. In case HUF is weaker, the price increases slightly, in case HUF is stronger, the price goes lower slightly.
- Discount 20% (cc. 5 446 Ft off)
- Discounted price 21 783 Ft (20 746 Ft + 5% VAT)
27 229 Ft
Availability
Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
Not in stock at Prospero.
Why don't you give exact delivery time?
Delivery time is estimated on our previous experiences. We give estimations only, because we order from outside Hungary, and the delivery time mainly depends on how quickly the publisher supplies the book. Faster or slower deliveries both happen, but we do our best to supply as quickly as possible.
Product details:
- Edition number 1st ed. 2021
- Publisher Springer
- Date of Publication 7 November 2022
- Number of Volumes 1 pieces, Book
- ISBN 9783030751760
- Binding Paperback
- No. of pages352 pages
- Size 235x155 mm
- Weight 563 g
- Language English
- Illustrations 7 Illustrations, black & white; 81 Illustrations, color 452
Categories
Short 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 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.
MoreLong 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.
?The book will appeal to a reader interested on the arithmetic aspects of some natural intersections and interactions between algebraic and convex geometry.? (Felipe Zaldívar, zbMATH 1483.13001, 2022) More
Table of Contents:
Introduction.- A brief history of points of infinity in geometry.- Quasiprojective varieties over algebraically closed fields.- Intersection multiplicity.- Convex polyhedra.- Toric varieties over algebraically closed fields.- Number of solutions on the torus: BKK bound.- Number of zeroes on the affine space I: (Weighted) Bézout theorems.- Intersection multiplicity at the origin.- Number of zeroes on the affine space II: the general case.- Minor number of a hypersurface at the origin.- Beyond this book.- Miscellaneous commutative algebra.- Some results related to schemes.- Notation.- Bibliography.
More
How Many Zeroes?: Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity
Subcribe now and receive a favourable price.
Subscribe
27 229 HUF
Endless Forms: The Secret World of Wasps
Subcribe now and receive a favourable price.
Subscribe
11 262 HUF
