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Introduction to tropical geometry /

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear fun...

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Bibliographic Details
Main Authors: Maclagan, Diane, 1974- (Author)
Group Author: Sturmfels, Bernd, 1962-
Published: American Mathematical Society,
Publisher Address: Providence, Rhode Island :
Publication Dates: [2015]
Literature type: Book
Language: English
Series: Graduate studies in mathematics ; v. 161.
Subjects:
Tropical geometry > Study and teaching (Graduate)
Geometry, Algebraic > Study and teaching (Graduate)
Summary: Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. --Provided by publisher.
Carrier Form: xii, 363 pages : illustrations ; 27 cm.
Bibliography: Includes bibliographical references (pages 351-359) and index.
ISBN: 9780821851982 (alkaline paper) :
0821851985 (alkaline paper)
Index Number: QA582
CLC: O187
Call Number: O187/M161
Contents: 1. Tropical Islands -- 2. Building Blocks -- 3. Tropical Varities -- 4. Tropical Rain Forest -- 5. Tropical Garden -- 6. Toric Connections.

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