
Tropical Algebraic Geometry
Birkhäuser Verlag GmbH
1st Edition
Published on 16. February 2007
Book
Paperback/Softback
VIII, 103 pages
978-3-7643-8309-1 (ISBN)
Article exhausted; check for reprint
Description
Tropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)-arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties. These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.
More details
Series
Language
English
Place of publication
Basel
Switzerland
Target group
Professional and scholarly
Illustrations
30
30 s/w Abbildungen, 30 s/w Zeichnungen
30 black & white illustrations, 30 black & white line drawings
Dimensions
Height: 24 cm
Width: 17 cm
Weight
259 gr
ISBN-13
978-3-7643-8309-1 (9783764383091)
Schweitzer Classification
Other editions
New editions

Book
04/2009
2nd Edition
Birkhäuser
€32.09
Shipment within 10-15 days
Content
Preface.- 1. Introduction to tropical geometry - Images under the logarithm - Amoebas - Tropical curves.- 2. Patchworking of algebraic varieties - Toric geometry - Viro's patchworking method - Patchworking of singular algebraic surfaces - Tropicalization in the enumeration of nodal curves.- 3. Applications of tropical geometry to enumerative geometry - Tropical hypersurfaces - Correspondence theorem - Welschinger invariants.- Bibliography.