Tropical Algebraic Geometry

2. Auflage 2009
ISBN: 978-3-0346-0047-7
Verlag: Birkhäuser Basel

Buch, Englisch, Band 35, 104 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 212 g

Reihe: Oberwolfach Seminars

These notes present a polished 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 notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

Zielgruppe

Research

Autoren/Hrsg.

Itenberg, Ilia

Shustin, Eugenii I.

Mikhalkin, Grigory

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.