An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
Algebraic and Analytic Geometry of Fans

Available Formats:
Electronic ISBN: 978-1-4704-0132-0
Product Code: MEMO/115/553.E
List Price: $44.00 MAA Member Price:$39.60
AMS Member Price: $26.40 Click above image for expanded view Algebraic and Analytic Geometry of Fans Carlos Andradas University of Cantabria Jesús M. Ruiz University Complutense de Madrid, Madrid, Spain Available Formats:  Electronic ISBN: 978-1-4704-0132-0 Product Code: MEMO/115/553.E  List Price:$44.00 MAA Member Price: $39.60 AMS Member Price:$26.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 1151995; 117 pp
MSC: Primary 14; 32;

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.

• Chapters
• Introduction
• 1. Basic and generically basic sets
• 2. The real spectrum
• 3. Algebraic and analytic tilde operators
• 4. Fans and basic sets
• 5. Algebraic fans and analytic fans
• 6. Prime cones and valuations
• 7. Centers of an algebraic fan
• 8. Henselization of algebraic fans
• 9. A going-down theorem, for fans
• 10. Extension of real valuation rings to the henselization
• 11. The amalgamation property
• 12. Algebraic characterization of analytic fans
• 13. Finite coverings associated to a fan
• 14. Geometric characterization of analytic fans
• 15. The fan approximation lemma
• 16. Analyticity and approximation
• 17. Analyticity after birational blowing-down
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1151995; 117 pp
MSC: Primary 14; 32;

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.

• Chapters
• Introduction
• 1. Basic and generically basic sets
• 2. The real spectrum
• 3. Algebraic and analytic tilde operators
• 4. Fans and basic sets
• 5. Algebraic fans and analytic fans
• 6. Prime cones and valuations
• 7. Centers of an algebraic fan
• 8. Henselization of algebraic fans
• 9. A going-down theorem, for fans
• 10. Extension of real valuation rings to the henselization
• 11. The amalgamation property
• 12. Algebraic characterization of analytic fans
• 13. Finite coverings associated to a fan
• 14. Geometric characterization of analytic fans
• 15. The fan approximation lemma
• 16. Analyticity and approximation
• 17. Analyticity after birational blowing-down
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.