<2025년 1학기 콜로퀴움> 

Title : Complex surfaces with minimal Betti numbers

Abstract : The surfaces in the title are complex surfaces with the Betti numbers of the complex projective plane, and are called (rational) homology projective planes. 

If such a surface has only quotient singularities (a kind of mild singularities), then its minimal resolution is a 2-dimensional complex manifold with zero geometric genus and irregularity. 

They are 2-dimensional generalizations of the complex projective line (the Riemann sphere), and are closely related to the theory of 4-manifolds. 

Fake projective planes and the complex projective plane are smooth examples of a rational homology projective plane. 

My presentation will begin with basic definitions and examples, and then describe recent progress in the study of such surfaces, singular ones and fake projective planes.