I am a graduate student in Mathematics and interested in Algebraic Geometry , In particular questions on Moduli Space . Now to start thinking about some problem for research what kind of question we may ask?
Are there any paper that will be very helpful?
How to start thinking about it.
Looking forward for help and suggestion.
I got problem posted on internet , like compatifying moduli space and motivic structure.
But I am not sure about those problem in initial research.
Hello,
You could try to understand the works of J. Ayoub, around the famous Konsevitch-Zagier conjecture.
Please visit this link you will get enough information
https://math.stanford.edu/~vakil/727/index.html
Thank you sir. Pleasure to read prof. vakil"s notes on algebraic geometry.
Hi Arindam, yes the advices from M. Nazrul are better than mine if you want to investigate precisely something about the moduli spaces.
Both topics are quite technical and abstract.
Your suggested paper is nice. Hope to understand it's application. I have read some notes from vakil...
Hello Arindam.
It seems the Stanford site have mentioned already Mumford's book:
"Curves on an algebraic surface", and Kodaira's work: "Deformation of complex algebraic varieties", among other valuable sources.
Questions you may ask... They will depend on what are you interested to work: algebraic curves, Riemann surfaces, manifolds, vector bundles, among others.
Perhaps a nice place to look, in terms of moduli spaces of vector bundles, is the seminal work of Atiyah & Bott:
"The Yang-Mills Equations over Riemann Surfaces"
Source: Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 308, No. 1505 (Mar. 17, 1983), pp. 523-615
Then, if you like Atiyah & Bott, maybe you can try Hitchin's work about the moduli space of Higgs bundles (holomorphic bundles with Higgs fields at the beginning):
"Self-duality equations over Riemann surfaces"
Source: Proc. London Math. Soc. (3) 55 (1987) 59-126.
There's also a very nice work about Hodge theory, Simpson's:
"Higgs bundles and local systems"
Source: Publications mathématiques de l'IHÉS, tome 75, (1992), 5-95.
I hope these references will be useful.
Many thanks for your suggestion Dr. Ronald Zuniga-Rojas . I will definitely look at what you have suggested.
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