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The index of degeneracy of a CM abelian variety can be arbitrarily large

Volume 202 / 2022

Masanari Kida, Hiromichi Yanai Acta Arithmetica 202 (2022), 55-66 MSC: 11G15, 14K22. DOI: 10.4064/aa210515-18-8 Published online: 15 December 2021

Abstract

For a simple abelian variety $A$, the index of degeneracy is the minimum $k$ such that the product $A^k$ holds an exceptional Hodge cycle. We show that for any positive integer $k$ there exists an abelian variety of CM-type with index of degeneracy $k$.

Authors

  • Masanari KidaDepartment of Mathematics
    Tokyo University of Science
    1-3 Kagurazaka, Shinjuku
    Tokyo 162-8601, Japan
    e-mail
  • Hiromichi YanaiCenter for General Education
    Aichi Institute of Technology Yakusa-cho
    Toyota 470-0392, Japan
    e-mail

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