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I'm sorry if this question sounds a little vague.

I'm about to finish Fulton's algebraic curves book and I would like to know what's next. I'm looking for something deeper in algebraic curves. I'm a beginner in this subject and I'm felling a little lost.

Is there an "obvious" next step after study Riemann-Roch theorem? or it's depending of the branch you follow? if does, which branches can I follow?

Thanks in advance!

user122342
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  • I've got Algebraic Curves and Riemann Surfaces by Rick Miranda on my shelf. I don't have Fulton so I can't compare them. – John Habert Feb 12 '14 at 02:11
  • @JohnHabert http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf – user122342 Feb 12 '14 at 02:13
  • Thanks for link. In trying to save it, I discovered I had downloaded it yesterday from another thread on here so I was wrong about not having Fulton. Miranda takes more time with general Riemann surfaces over complex numbers before moving to Riemann-Roch and related theorems. Book ends with sheaves and cohomology. – John Habert Feb 12 '14 at 02:31

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