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Riemann Surfaces and Algebraic Curves
Riemann Surfaces and Algebraic Curves
A first course in Hurwitz Theory
This textbook written with Eric Miles is intended for an higher level undergraduate course or an introductory graduate course. Its main goal is to use Hurwitz theory to illustrate how many different areas of mathematics can "play together" in higher level mathematics.
Errata
Errata
(Many thanks to Dustin Ross, Elzbieta Polak and Trieste Desautels for catching them!)
page 12, third bullet point: the radii r_1 and r_2 need to be equal.
page 76, Exercise 5.3.1: the images of two different lifts need not be disjoint. The correct statement is that the set of values where the functions agree is either everything or the empty set.
page 76, Lemma 5.3.5 and Figure 5.9: the roles of X and Y are reversed between the text and the figure, which then leads also to an inconsistency in the last sentence of the Lemma, "Repeat this process using..."
page 93, Example 7.1.3: the second, third and fourth lifts should have (t+1)i instead of (ti+1), (t+2)i instead of (ti+2), etc.
page 117, Table 8.1: the bottom right entry of the character table of S_3 is -1.
Tropical And Logarithmic Methods in Enumerative Geometry
Tropical And Logarithmic Methods in Enumerative Geometry
Written with Hannah Markwig and Dhruv Ranganathan, this textbook collects the work accumulated in many summer schools, master classes and an MFO seminar. It provides an introduction to the interactions between tropical and logarithmic geometry with an eye towards applications to enumerative geometric problems. While the book is a bit "rougher" than we intended it to be, we hope it can be useful for graduate students that are interested in entering the area.
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