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We give a self-contained introduction into logarithmic deformation theory. We explain how the construction of Calabi–Yau manifolds and in particular the toric Gross–Siebert mirror construction motivate logarithmic deformation theory. We give an overview over the basic concepts and main results discussed in this monograph and outline some of the arguments. In particular, we illustrate the concept of singularities in logarithmic geometry with many examples, and we explain how the logarithmic version of the Bogomolov–Tian–Todorov theorem allows us to smooth reducible schemes. At the end of this chapter, we give an outlook on questions that remain unaddressed.

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Introduction

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  • 发表日期：

    2025年

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  • Simon Felten

摘要

We give a self-contained introduction into logarithmic deformation theory. We explain how the construction of Calabi–Yau manifolds and in particular the toric Gross–Siebert mirror construction motivate logarithmic deformation theory. We give an overview over the basic concepts and main results discussed in this monograph and outline some of the arguments. In particular, we illustrate the concept of singularities in logarithmic geometry with many examples, and we explain how the logarithmic version of the Bogomolov–Tian–Todorov theorem allows us to smooth reducible schemes. At the end of this chapter, we give an outlook on questions that remain unaddressed.