We construct three nonsingular threefolds X, X′ and X′′ with vanishing irregularities. The threefold X has Kodaira dimension = κ(X) = 1 and its m-canonical transformation is such that its image has dimension 1 for each m ≥ 32 (and not for m = 31). The threefolds X′ and X′′ have Kodaira dimension κ(X′) = κ(X′′) = 2 and their m-canonical transformations φ_m are such that φ_m(X') has dimension 2 if and only if m ≥ 12 and φ_m(X'') has dimension 2 if and only if m = 9, 10 or m ≥ 12.
Examples of threefolds with Kodaira dimension 1 or 2
CALABRI, Alberto;
2011
Abstract
We construct three nonsingular threefolds X, X′ and X′′ with vanishing irregularities. The threefold X has Kodaira dimension = κ(X) = 1 and its m-canonical transformation is such that its image has dimension 1 for each m ≥ 32 (and not for m = 31). The threefolds X′ and X′′ have Kodaira dimension κ(X′) = κ(X′′) = 2 and their m-canonical transformations φ_m are such that φ_m(X') has dimension 2 if and only if m ≥ 12 and φ_m(X'') has dimension 2 if and only if m = 9, 10 or m ≥ 12.File in questo prodotto:
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