Ramified Surfaces: On Branch Curves and Algebraic Geometry in the 20th Century

Michael Friedman - Collection Yellow Sale 2024

252 pages, parution le 27/09/2022

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Résumé

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19^th century with descriptive geometry as well as knot theory, the book focuses on the 20^th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon's program of braid monodromy factorization.

By focusing on how the research on one specific curve changed during the 20^th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20^th century, considering this curve as an intersection of several research approaches and methods.

Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.

Chapter 1: Introduction.- Chapter 2: Prolog: Separate beginnings during the 19th century.- Chapter 3: 1900s-1930s: Branch curves and the Italian school of algebraic geometry.- Chapter 4: Chisini's branch curves: the decline of the classical approach.- Chapter 5. From the 1970s onwards: the rise of braid monodromy factorization.-Chapter 6: Epilogue: On ramified and ignored spaces.

Michael Friedman is a historian of mathematics and a senior lecturer at the Tel Aviv University. The focus of his research is how material, visual and symbolical knowledge and practices in mathematics interact with each other. More specifically, his research examines how material practices (folding, weaving, braiding, knotting, as well as three-dimensional models) prompt symbolical mathematical knowledge. Recent publications: A History of Folding in Mathematics. Mathematizing the Margins (Birkhauser, 2018).