Remarks on Kawamata’s Effective Non-vanishing Conjecture for Manifolds with Trivial First Chern Classes
نویسنده
چکیده
Abstract. Kawamata proposed a conjecture predicting that every nef and big line bundle on a smooth projective variety with trivial first Chern class has nontrivial global sections. We verify this conjecture for several cases, including (i) all hyperkähler varieties of dimension ≤ 6; (ii) all known hyperkähler varieties except for O’Grady’s 10-dimensional example; (iii) general complete intersection Calabi–Yau varieties in certain Fano manifolds (e.g. toric ones). Moreover, we investigate the effectivity of Todd classes of hyperkähler varieties and Calabi– Yau varieties. We prove that the fourth Todd classes are “fakely effective” for all hyperkähler varieties and general complete intersection Calabi–Yau varieties in products of projective spaces.
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