Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE DETERMINANT OF A DUAL PERIODIC SINGULAR FIBER

  • Cheng Gong (Department of Mathematics Soochow University) ;
  • Jun Lu (Department of Mathematics Shanghai Key Laboratory of PMMP East China Normal University) ;
  • Sheng-Li Tan (Department of Mathematics Shanghai Key Laboratory of PMMP East China Normal University)
  • Received : 2022.10.11
  • Accepted : 2023.02.24
  • Published : 2023.09.30
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Abstract

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.

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References

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