Summer Lectures in Geometry   RSS

24/07/2012, 15:45 — 16:45 — Room P3.10, Mathematics Building
, Korean Institute for Advanced Study

Fake projective planes

It is known that a compact complex manifold of dimension 2 with the same Betti numbers as the complex projective plane is projective. Such a manifold is called "a fake projective plane" if it is not isomorphic to the complex projective plane. So a fake projective plane is exactly a smooth surface X of general type with p g(X)=0 and c 1(X) 2=3c 2(X)=9. By a result of Aubin and Yau, its universal cover is the unit 2-ball, hence its fundamental group π 1(X) is a discrete torsion-free cocompact subgroup of PU(2,1) satisfying certain conditions. The classification of such subgroups has been done by G. Parasad and S.-K. Yeung, with the computer based computation by D. Cartwright and J. Steger. This has settled the arithmetic side of the classification problem. I will go over this, and then report recent progress on the other side of the problem-geometric construction.
Session 2

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