• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1365-1374
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• 2023

Let F be a periodic singular fiber of genus g with dual fiber F^*, and let T (resp. T^*) be the set of the components of F (resp. F^*) by removing one component with multiplicity one. We give a formula to compute the determinant | det T | of the intersect form of T. As a consequence, we prove that | det T | = | det T^*|. As an application, we compute the Mordell-Weil group of a fibration f : S → ℙ¹ of genus 2 with two singular fibers.