On integral Hodge classes on uniruled or Calabi-Yau threefolds
نویسنده
چکیده
Let X be a smooth complex projective variety of dimension n. The Hodge conjecture is then true for rational Hodge classes of degree 2n−2, that is, degree 2n−2 rational cohomology classes of Hodge type (n − 1, n − 1) are algebraic, which means that they are the cohomology classes of algebraic cycles with Q-coefficients. Indeed, this follows from the hard Lefschetz theorem, which provides an isomorphism:
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