Heesang Park, Jongil Park and Dongsoo Shin
نویسنده
چکیده
This paper is an addendum to [4], in which the authors constructed a simply connected minimal complex surface of general type with pg = 0 and K 2 = 3. Motivated by Y. Lee and the second author’s recent construction on a surface of general type with pg = 0, K 2 = 2 and H1 = Z/2Z [3], we extend the result to the K = 3 case in this paper. That is, we construct a new non-simply connected minimal surface of general type with pg = 0, K 2 = 3 and H1 = Z/2Z using a rational blow-down surgery and a Q-Gorenstein smoothing theory. The key ingredient of this paper is to find a right rational surface Z which makes it possible to get such a complex surface. Once we have a right candidate Z for K = 3, the remaining argument is similar to that of K = 3 case appeared in [4]. That is, by applying a rational blow-down surgery and a Q-Gorenstein smoothing theory developed in [2] to Z, we obtain a minimal complex surface of general type with pg = 0 and K 2 = 3. Then we show that the surface has H1 = Z/2Z by using a similar method in [3]. Since almost all the proofs are parallel to the case of the main construction in [4, §3], we only explain how to construct such a minimal complex surface. The main result of this paper is the following
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