Elliptic surfaces over a genus 2 curve. II (Q1327753)

[For part I see Math. Jap. 40, No. 3, 547-552 (1994; see the preceding abstract).] The classification of minimal elliptic surfaces over a given curve and with a given number of singular fibers has interested various authors. The paper under review is one of a series of articles by the author on this subject. In this paper are classified minimal elliptic surfaces \(\pi : X \to C\), over a genus 2 curve with a section and exactly one singular fiber of type \(I^*_6\). Such classification has been done under the following assumptions: (a) the \(J\)-map \(J : C \to \mathbb{P}^1\) associated to the fibration factors either through the canonical map \(\varphi_K : C \to \mathbb{P}^1\) or it factors through a triple cover of \(\mathbb{P}^1\); (b) \(J^{-1} (1)\) is either one point of multiplicity 6 or three points each of multiplicity 2. The classification was accomplished by finding at first all possibilities for the ramification of the \(J\)-map. These information were then used to build up the desired surfaces.