A study on rational homology projective planes

A normal projective surface with the same Betti numbers of the projective plane ℂℙ2 is called a rational homology projective plane or a ℚ-homology ℂℙ2. People working in algebraic geometry and topology have long studied a ℚ-homology ℂℙ2 with possibly quotient singularities. It is now known that it has at most five such singular points, but it is still mysterious so that there are many unsolved problems left. In this talk, I’ll review some known results and open problems in this field which might be solved and might not be solved in near future. In particular, I’d like to review the following two topics and to report some recent progress:

1. Algebraic Montgomery-Yang problem.

2. Classification of ℚ-homology ℂℙ2 with quotient singularities.

This is a joint work with Woohyeok Jo and Kyungbae Park.