SOME RECENT TOPICS IN SMOOTHABLE STABLE LOG SURFACES

Abstract. This is an introductory article of the study of smoothable stable log surfaces. First we briefly introduce the projectivity of the moduli functor of smoothable stable log surfaces with given Hilbert function. The positivity of the second Chern class of stable log surfaces and its relation of boundedness are discussed. Also the study of limits of plane curves by using smoothable stable log surfaces, and the construction of surfaces by using smoothable stable surfaces are shortly discussed. It has been known for a long time that the set of all curves of a fixed genus g nat-urally corresponds to the points on a certain variety with dimension 3g−3, which is denoted by Mg. The moduli space Mg is not projective, and there has been consid-erable work in finding a natural compactification. What kind of curves correspon