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Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.

Pietro Sabatino (2005)

Revista Matemática Complutense

Let X ⊂ P6 be a smooth irreducible projective threefold, and d its degree. In this paper we prove that there exists a constant β such that for all X containing a smooth ruled surface as hyperplane section and not contained in a fourfold of degree less than or equal to 15, d ≤ β. Under some more restrictive hypothesis we prove an analogous result for threefolds containing a smooth ruled surface as hyperplane section and contained in a fourfold of degree less than or equal to 15.

Bounds on the denominators in the canonical bundle formula

Enrica Floris (2013)

Annales de l’institut Fourier

In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If r is the Cartier index of the fibre, it was expected that 12 r would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in r , we provide a bound N ( r ) and an example where the smallest integer that clears the denominators of the moduli part is N ( r ) / r . Moreover we prove that even locally the denominators depend...

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