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2 results

  • A REMARK ON FUJINO’S WORK ON THE CANONICAL BUNDLE FORMULA VIA PERIOD MAPS

  • Part of
  • HYUNSUK KIM
  • Journal:
    Nagoya Mathematical Journal , First View
    Published online by Cambridge University Press:
    02 December 2024, pp. 1-14
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  • Fujino gave a proof for the semi-ampleness of the moduli part in the canonical bundle formula in the case when the general fibers are K3 surfaces or abelian varieties. We show a similar statement when the general fibers are primitive symplectic varieties. This answers a question of Fujino raised in the same article. Moreover, using the structure theory of varieties with trivial first Chern class, we reduce the question of semi-ampleness in the case of families of K-trivial varieties to a question when the general fibers satisfy a slightly weaker Calabi–Yau condition.

  • The Tate Conjecture for Cubic Fourfolds over a Finite Field

  • Norman Levin
  • Journal:
    Compositio Mathematica / Volume 127 / Issue 1 / May 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 1-21
    Print publication:
    May 2001
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  • We prove the Tate conjecture for codimension 2 cycles on an ordinary cubic fourfold over a finite field. The proof involves the construction of canonical coordinates on the formal deformation space via a crystalline period map.