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- W3100804203 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 hyperk{a}hler varieties of dimension $leq 6$; (ii) all known hyperk{a}hler 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 hyperk{a}hler varieties and Calabi-Yau varieties. We prove that the fourth Todd classes are fakely effective for all hyperk{a}hler varieties and general complete intersection Calabi-Yau varieties in products of projective spaces." @default.
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- W3100804203 date "2019-12-13" @default.
- W3100804203 modified "2023-09-25" @default.
- W3100804203 title "Remarks on Kawamata’s effective non-vanishing conjecture for manifolds with trivial first Chern classes" @default.
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- W3100804203 doi "https://doi.org/10.1007/s00209-019-02455-x" @default.
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