Abundance Theorem for Semi Log Canonical Threefolds

for semi log canonical threefolds. The abundance conjecture is a very important problem in the birational classi cation of algebraic varieties. The abundance theorem for semi log canonical surfaces was proved in [12, Chapter 8, 12] by L.-Y. Fong, S. Keel, J. Koll ar, and J. McKernan. Their proof uses semiresolution, etc. and has some combinatorial complexities. So we simplify their proof and strengthen the theorem for semi divisorial log terminal surfaces a little (See Corollary (4.8)). By our method we can reduce the problem to the irreducible case and the niteness of some groups. This shows that if the log Minimal Model