“The book under review is a motivated by a series of recent results in the context of the problem of resolution of families and semistable reduction … . the authors have organized the book in seven chapters, where the classical ideas and the main tools of this different framework are presented. … A very comprehensive collection of references is given at the end of each chapter.” (Ana Bravo, zbMATH 1545.14001, 2024)
New Techniques in Resolution of Singularities
von Dan Abramovich, Anne Frühbis-Krüger, Michael Temkin und Jarosław WłodarczykResolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced.
The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.
