Tropical Algebraic Geometry

• Main Authors: Itenberg, Illia (Author), Mikhalkin, Grigory (Author), Shustin, Eugenii (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2009.
• Series: Oberwolfach Seminars ; 35
• Subjects: Mathematics.; Algebraic geometry.; Algebraic Geometry.

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...

Table of Contents:

• 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.