TY  - BOOK
AU  - Itenberg,Ilia
AU  - Mikhalkin,Grigory
AU  - Shustin,Eugenii
ED  - SpringerLink (Online service)
TI  - Tropical Algebraic Geometry
T2  - Oberwolfach Seminars,
SN  - 9783764383107
AV  - QA564-609 
U1  - 516.35 23
PY  - 2007///
CY  - Basel
PB  - Birkhäuser Basel
KW  - Geometry, algebraic
KW  - Algebraic Geometry
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-7643-8310-7
ER  -