Renzo Cavalieri,Hannah Markwig,Dhruv Ranganathan
Tropical and Logarithmic Methods in Enumerative Geometry
Tropical and Logarithmic Methods in Enumerative Geometry
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- More about Tropical and Logarithmic Methods in Enumerative Geometry
The book covers logarithmic Gromov-Witten theory, tropical geometry, and the degeneration formula for Gromov-Witten invariants, with examples and calculations. It provides an assisted entry route to the subject for readers.
Format: Paperback / softback
Length: 159 pages
Publication date: 02 October 2023
Publisher: Birkhauser Verlag AG
Logarithmic Gromov-Witten theory is a fundamental concept in modern approaches to mirror symmetry and has opened up numerous new directions in enumerative geometry. Tropical geometry provides a powerful calculus for carrying out calculations in this field, and these notes cover the foundational aspects of tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and practical nuances of working with and enumerating tropical curves. Readers will gain an assisted entry route to the subject, focusing on examples and explicit calculations.
The book is based on lectures given at the Oberwolfach Seminar held in Fall 2021, and it covers a wide range of topics related to logarithmic Gromov-Witten theory and tropical geometry. The first chapter provides an introduction to logarithmic Gromov-Witten theory, including its history, motivation, and applications. It also introduces the basic concepts of tropical geometry, such as tropical curves, tropical varieties, and tropical linear spaces.
The second chapter focuses on the degeneration formula for Gromov-Witten invariants. It discusses the degeneration of tropical curves and the corresponding degeneration of Gromov-Witten invariants. It also provides examples of how to use the degeneration formula to calculate Gromov-Witten invariants of various types of tropical curves.
The third chapter covers geometric aspects of the degeneration formula for Gromov-Witten invariants. It discusses the geometry of tropical curves and tropical varieties, including their moduli spaces and their intersection theory. It also provides examples of how to use the geometry of tropical curves to calculate Gromov-Witten invariants of various types of tropical curves.
The fourth chapter covers practical nuances of working with and enumerating tropical curves. It discusses the algorithms and software used for calculating tropical curves and Gromov-Witten invariants, as well as the techniques used for enumerating tropical curves. It also provides examples of how to use these techniques to solve problems in enumerative geometry.
In conclusion, this book is a valuable resource for anyone interested in logarithmic Gromov-Witten theory and tropical geometry. It provides a comprehensive introduction to the subject, covering the foundational aspects of tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and practical nuances of working with and enumerating tropical curves. Readers will gain an assisted entry route to the subject, focusing on examples and explicit calculations.
Dimension: 240 x 168 (mm)
ISBN-13: 9783031394003
Edition number: 1st ed. 2023
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