Effective Non-vanishing for Fano Weighted Complete Intersections
نویسندگان
چکیده
We show that Ambro–Kawamata’s non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X , then |H | is not empty. If X is smooth, we further show that the general element of |H | is smooth. We then verify Ambro–Kawamata’s conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita’s freeness conjecture for a Gorenstein quasismooth weighted hypersurface. For the proofs, we introduce the arithmetic notion of regular pairs and enlighten some interesting connection with the Frobenius coin problem.
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