Classification Of The Singular Fibers With Small Signature

The classification of singular fiber has a long history and play an active role in the development of algebraic geometry. It is interesting also. But it is hard to attack. In this article, we use the techniques developed from indicated by Prof. S.-L. Tan and coauthor Lu. In that paper, Prof. Tan and Lu developed easy formulae for the computation of Chern numbers and also relate these computation with some invariants of modulii. By computation of particular divisors, we give a classification of the minimal singular fibers satisfying the condition that8<2c2(F)-c12(F)≤12.In the progress we discover that the minimal singular fibers satisfying the con-dition that8<2c2(F)-c12(F)≤12. are rare and of special type. And also we also find that F has no non-ADE singu-larity. We can give an simple explanation based on the fact that the value ap and2μp-αp+βP are both large in the non-ADE case.