Algebraic and Analytic Geometry of Fans (Memoirs of the American Mathematical Society)

Andradas, Carlos, Ruiz, Jesus M.

ISBN 10: 0821826123 / ISBN 13: 9780821826126

Published by Amer Mathematical Society, 1995

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Bibliographic Details

• Title: Algebraic and Analytic Geometry of Fans (Memoirs of the American Mathematical Society)
• Publisher: Amer Mathematical Society
• Publication Date: 1995
• Language: English
• ISBN 10: 0821826123
• ISBN 13: 9780821826126
• Binding: paperback
• Condition: Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

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Synopsis

A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a description is possible locally around every point, by means of analytic inequalities varying with the point, the set is called semianalytic. If one single system of strict inequalities is enough, either globally or locally at every point, the set is called basic. The topic of this work is the relationship between these two notions. Namely, Andradas and Ruiz describe and characterize, both algebraically and geometrically, the obstructions for a basic semianalytic set to be basic semialgebraic. Then they describe a special family of obstructions that suffices to recognize whether or not a basic semianalytic set is basic semialgebraic. Finally, they use the preceding results to discuss the effect on basicness of birational transformations.