November 11, 1986 Dear ShingTung: Thank you for your letter of November 6, 1986. In response to your letter I would like to bring up a few points. 1. In my talk in Columbia I presented my method of proving the existence of KahlerEinstein metrics on compact Kahler manifolds with positive anticanonical line bundle and a suitable finite group of symmetry. I mentioned at the end that I was still checking some concrete examples. Right after my return to Harvard I verified the case of the Fermat cubic surface. Within two weeks after the Columbia Conference a typed manuxxxx was available. Morris Kalka and PitMann Wong had copies at that time. When I looked over my manuxxxx to prepare my talk in Paris in June I added the examples of blowing up three point in and higherdimensional Fermat hypersurfaces. All those examples were verified before last summer. In any case what is important is the method. Checking concrete examples is only the simple task of counting the degrees of certain curves and the number of points of the curves belonging to the same orbit. 2. Concerning your student’s independent derivation of the equivalence of and , I would like to point out that the equivalence of bounds for , , , , , and was already in the handwritten notes entitled “Reflection Methods” which I sent you about nine years ago. That was way before your student came to the Unites States. Even a few year later you mentioned to me that you were still keeping those notes. Unless in your discussions with your students you were deliberately keeping back from them what you already knew, I do not see how independent your student’s derivation can be. 3. Since I have not seen your student’s manuxxxx, it is impossible for me to determine exactly how much your student’s method is similar to or different from the one I presented at the Columbia Conference. However, from the inxxxxation that I have, it seems to me that his method is essentially a rexxxxulation using the equivalent bound of . It is against my nature to argue over priorities (and as a matter of fact to argue over anything). I always pride myself on being fair and careful in such matters. In this case I was rather upset to learn what seems to be somebody claiming as his own a rexxxxulation of a method of mine already presented in public lectures. Since according to a number of people your student’s manuxxxx is available, it seems that the easiest way to clarify this is for me to have a look at a copy of this manuxxxx. Best regard, YumTong Siu
