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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.

20 votes
2 answers
5k views

What does the Jacobian of a curve tell us about the curve?

A natural object in the study of curves is the Jacobian of a curve. What are some natural geometric properties of the curve that the Jacobian encapsulates? In other words, what can the Jacobian tell u …