Tropical and Logarithmic Methods in Enumerative Geometry
Buch in deiner Nähe kaufen
Beschreibung
This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.
This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.
Provides a review and introduction of each of these 3 fields with a particular eye to the interactions Provides hands-on exercises, plenty of examples and pictures The interplay of tropical, logarithmic and enumerative geometry presented is original
Autor*in
Renzo Cavalieri
Themen in »Tropical and Logarithmic Methods in Enumerative Geometry«
Tropical Geometry Correspondence Theorems Gromov-Witten Theory ELSV-Formula Moduli Spaces Enumerative Geometry Logarithmic Geometry Hurwitz Theory Caporaso-Harris Recursion Tropical Compactifications Toric Varieties
Stimmen zu »Tropical and Logarithmic Methods in Enumerative Geometry«
“The book gives many technical details, along with examples and exercises for readers to familiarize themselves with the techniques. After reading it, and answering the exercises, readers should have a good basis for understanding recent papers approaching enumerative geometry with logarithmic and tropical methods.” (Reinier Kramer, Mathematical Reviews, April, 2025)
“The book consists of three parts written by three different authors … . there is a small number of cross-references within the text, the parts are largely independent and can be read separately in an arbitrary order. Each of them may serve as an excellent introduction to the corresponding topic … .” (Mikhail Shkolnikov, zbMATH 1544.14001, 2024)
()