|場所：||京都大学数理解析研究所 202 号室|
|Gopal Prasad 氏 （University of Michigan）|
|題目：||Fake projective planes|
A fake projective plane is a smooth compact complex surface
which is not the complex projective plane but has the same Betti
numbers as the complex projective plane. The first fake projective
plane was constructed by David Mumford in 1979 using p-adic
uniformization. Two more examples were found by M.Ishida and F.Kato
using a similar idea. Just recently JongHae Keum has given an example
which may be different from the three known examples.
In a joint work with Sai-Kee Yeung, I have given seventeen finite families of examples of fake projective planes and shown that these, and possibly three more, exhaust them.
In another joint work with Sai-Kee Yeung I have studied quotients of the complex ball of dimension n by cocompact arithmetic subgroups of PU(n,1), and shown that except for n = 2 and 4, there are no quotients whose Betti numbers equal that of complex projective space of dimension n. If n = 4 there are four nonisomorphic quotients which have same Betti numbers as P^4.
I will give an exposition of these results for a general mathematical audience.