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

Acknowledgements
Contents
1: Introduction
	1.1 On Branch Points and Branch Curves
	1.2 Dynamics of a Mathematical Object
		1.2.1 Ephemeral Epistemic Configurations and the Identity of the Mathematical Objects
		1.2.2 On Branch Points, Again: on Riemann´s Terminology and How (Not) to Transfer Results
		1.2.3 On Branch Curves, Again: Plurality of Notations
		1.2.4 Transformations Between Epistemic Configurations
	1.3 An Overview: Historical Literature, Structure and Argument
		1.3.1 Omitted Traditions
		1.3.2 Structure of the Book: The Twentieth Century
2: Prologue: Separate Beginnings During the Nineteenth Century
	2.1 The Beginning of the Nineteenth Century: Monge and the ``Contour Apparent´´
	2.2 1820s-1860s: Étienne Bobillier and George Salmon
	2.3 1890s-1900s: Wirtinger´s and Heegaard´s Turn Towards Knot Theory
	2.4 The End of the Nineteenth Century: A Regression Toward the Local
3: 1900s-1930s: Branch Curves and the Italian School of Algebraic Geometry
	3.1 Enriques: A Plurality of Methods to Investigate the Branch Curve
		3.1.1 Enriques on Intuition and Visualization
		3.1.2 The Turn of the nineteenth Century: First Attempts of Classification of Surfaces
			3.1.2.1 On Double Covers and Branch Curves
			3.1.2.2 End of the 1890s: Enriques´s Initial Configurations
		3.1.3 Two Papers from 1912 and the Culmination of the Classification Project
		3.1.4 1923: After the Classification Project
	3.2 Zariski and Segre: Novel Approaches
		3.2.1 The Late 1920s: Zariski on Existence Theorems and the Beginning of a Group-Theoretic Approach
		3.2.2 1930: Segre and Special Position of the Singular Points
		3.2.3 1930-1937: Before and After Zariski´s Algebraic Surfaces
			3.2.3.1 1935: Zariski´s Algebraic Surfaces
			3.2.3.2 After Algebraic Surfaces
	3.3 Reflections on Rigor: Reassessment and New Definitions in the 1950s
	3.4 Appendix to Chap. 3: Birational Maps and Genera of Curves and Surfaces
4: 1930s-1950s: Chisini´s Branch Curves: The Decline of the Classical Approach
	4.1 The 1930s and Chisini´s First Conjecture
		4.1.1 The ``Characteristic Bundle´´
		4.1.2 On Braids, Branch Curves and Degenerations
			4.1.2.1 Bernard d´Orgeval in Oflag X B
			4.1.2.2 Guido Zappa´s degenerations
		4.1.3 Detour. 1944: Chisini´s First `Conjecture´
	4.2 Chisini´s Students: Isolation and Abandonment
		4.2.1 Dedò and the New Notation of Braids
		4.2.2 Tibiletti and the Second `Theorem´ of Chisini
	4.3 Conclusion: Seclusion, Ignorance and Abandonment
	4.4 Appendix to Chap. 4: A Short Introduction to the Braid Group
5: From the 1970s Onward: The Rise of Braid Monodromy Factorization
	5.1 The 1960s: Generalization and Stagnation or the ``Rising Sea´´ and the Sunken Branch Curves
		5.1.1 Detour: End of the 1950s: Abhyankar´s Conjecture
		5.1.2 1971: The New Edition of Zariski´s Algebraic Surfaces
	5.2 The 1970s: Livne and Moishezon on Equivalence of Factorizations
		5.2.1 Livne´s MA Thesis from 1975
		5.2.2 Separations of Configurations and Shifts of Contexts
		5.2.3 On Surfaces with  and Livne´s 1981 PhD Thesis
	5.3 Moishezon´s Program
		5.3.1 From the USSR to Israel and to the USA
			5.3.1.1 Moishezon's Emigration and Jewish Mathematicians in the USSR
		5.3.2 Before Braid Monodromy: The Shafarevich School, Moishezon and the Decomposition of Algebraic Surfaces
		5.3.3 From 1981 to 1985: (Re)introducing Braid Monodromy
			5.3.3.1 1981: The Search for Normal Forms
			5.3.3.2 1983/1985: The Arithmetic of Braids and the Language of Factorizations
			5.3.3.3 Conclusion: Moishezon and Chisini
	5.4 Moishezon and Teicher Cross the Watershed
		5.4.1 Coda: The Group-Theoretical Approach of the 1990s
6: Epilogue: On Ramified and Ignored Spaces
Bibliography
Index