Quiz on Algebraic Curves and Moduli

We had a fun* quiz show format final exam for our course on Algebraic Curves.

*Well, I had a lot of fun in making it and then testing it out with Julian and then hosting it. I hope the students also enjoyed it.

The philosophy behind it was that I wanted my students to see what kind of things they can easily compute on spot with theorems like Riemann-Roch and Hurwitz’s formula and also to make them aware of easy pitfalls and common misconceptions that one can have with invariants like Hilbert polynomials or representable functors.

The grading scheme was

  • -1 if you pass a question without attempting
  • 0 if you say something which makes no sense at all, i.e its completely irrelevant**
  • 1 if you said something which was wrong completely, like a misconception, but you tried, basic mistakes would be given zero.
  • 2 if you said something which was partially right, like a part of the question or you made a mistake in the computation that you could not correct even with hints till the time was over.
  • 3 you got everything right about the question.
  • 4 you found a mistake in the question or the answer I gave.

**I think I should have divided this into two sub cases and marked -2 in case they used this option to tell me their favorite song as an answer to a question about algebraic curves and 0 should have been used if they made a basic mistake, like using a theorem where even its assumptions are not satisfied.

I adopted this grading scheme to make sure that they do try to attempt the question and don’t just pass it on. I had seen them not answering very easy questions in class and I was not going to let them get away with it in exams for free. There is no fun if you don’t even try. Mathematicians are not known to play safe.

In case you are curious about the quiz, here it is:

References for the Quiz

Listed in the order of frequency of their use.

  • Hartshorne, Algebraic Geometry, Springer, GTM 52, 1977.
  • Liu, Algebraic Geometry and Arithmetic Curves, Oxford University Press, OGTM 6, 2002.
  • Arbarello, Cornalba, Griffiths, Geometry of Algebraic Curves, volume 2, Springer, Grundlehren der mathematischen Wissenschaften, 268, 2011.
  • Eisenbud, Harris, 3264 and All That, Cambridge University Press, 2016.
  • Eisenbud, Harris, The Geometry of Schemes, Springer, GTM, 197, 2000.
  • Harris, Morrison, Moduli of curves, Springer GTM, 187, 1998.
  • Kock,  Vainsencher, An Invitation to Quantum Cohomology, Progress in Mathematics, 249, Birkhäuser Basel, 2007.

Quiz Results

The students did really well 🎉 🎉🎉and our audience (which consisted of Jan) had fun.

Acknowledgements

I would like to thank Julian Lyczak for his help in checking out the quiz and also for asking me really good questions in the class. I would like to thank my students who even came to classes virtually in corona semester and agreed to participate in quiz and also caught my mistakes, they are Kamil Rychlewicz, Maria Anna Sisak and Alec Shute. And lastly to Tamas Hausel for encouraging me to teach this course and IST graduate school for helping in organizing this course.