Tropical and Logarithmic Methods in Enumerative Geometry

Download or read book Tropical and Logarithmic Methods in Enumerative Geometry written by Renzo Cavalieri and published by Springer Nature. This book was released on 2023-11-01 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.