Ramified surfaces : on branch curves and algebraic geometry in the 20th century / Michael Friedman.
2022
QA564
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Details
Title
Ramified surfaces : on branch curves and algebraic geometry in the 20th century / Michael Friedman.
ISBN
9783031057205 (electronic bk.)
3031057201 (electronic bk.)
9783031057199
3031057198
3031057201 (electronic bk.)
9783031057199
3031057198
Published
Cham, Switzerland : Springer, 2022.
Language
English
Description
1 online resource : illustrations (black and white, and color).
Item Number
10.1007/978-3-031-05720-5 doi
Call Number
QA564
Dewey Decimal Classification
516.3/5
Summary
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 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th 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 Moishezons program of braid monodromy factorization. By focusing on how the research on one specific curve changed during the 20th 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 20th 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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Frontiers in the history of science.
Available in Other Form
Ramified surfaces.
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Table of Contents
Chapter 1: Introduction
Chapter 2: Prolog: Separate beginnings during the 19th century
Chapter 3: 1900s1930s: Branch curves and the Italian school of algebraic geometry
Chapter 4: Chisinis 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.
Chapter 2: Prolog: Separate beginnings during the 19th century
Chapter 3: 1900s1930s: Branch curves and the Italian school of algebraic geometry
Chapter 4: Chisinis 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.