Tropical Algebraic Geometry

• Κύριοι συγγραφείς: Itenberg, Ilia (Συγγραφέας), Mikhalkin, Grigory (Συγγραφέας), Shustin, Eugenii (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2007.
• Σειρά: Oberwolfach Seminars ; 35
• Θέματα: 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...

Πίνακας περιεχομένων:

• 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.