Titlebook: Ramified Surfaces; On Branch Curves and Michael Friedman Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license

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Introduction,rs of the pure shadows” are the only curves necessary to draw accurately, and in a certain sense, whose properties are the only ones one should know exactly. An example of what should be drawn is given by Monge, as can be seen in Fig. 1.1, when the source of “light” is either a point or a spherical

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,1900s–1930s: Branch Curves and the Italian School of Algebraic Geometry, these beginnings—and others—into a more unified research tradition concerning the branch curve. A significant role was played by the Italian school of algebraic geometry which, between the 1890s and 1930s, contributed greatly to the research on algebraic surfaces and, as a result, to the understand

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,1930s–1950s: Chisini’s Branch Curves: The Decline of the Classical Approach,es. Moreover, the importance of their works to the rise of Italian algebraic geometry during the first decades of the twentieth century is studied in several works. Though both died later, in 1946 and 1952, respectively, the period of greatest creativity of the Italian school of algebraic geometry e

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From the 1970s Onward: The Rise of Braid Monodromy Factorization,guage was inadequate and that a thorough rewriting in algebraic terms was needed. In Sect. ., we saw how Zariski and Weil considered their own rewriting projects with commutative algebra. However, after the reshaping of algebraic geometry in terms of the language of commutative algebra, in the 1950s

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2662-2564 a unique mathematical object: the branch curve.Delivers an .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. cent

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