Explicit equations of a fake projective plane.
Explicit equations of a fake projective plane.

Lev Borisov, Rutgers University
Fine Hall 322
Fake projective planes are complex algebraic surfaces of general type whose Betti numbers are the same as that of a usual projective plane. The first example was constructed by Mumford about40 years ago by 2adic uniformization. There are 50 complex conjugate pairs of such surfaces, given explicitly as ball quotients (Cartwright+Steger). However, a ball quotient description does not on its own lead to an explicit projective embedding. In a joint work with JongHae Keum, we find equations of one pair of fake projective planes in bicanonical embedding, which is so far the only result of this kind.