Bounds on the denominators in the canonical bundle formula

In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose generic fibre is a rational curve. In particular we find a bound for the denominators of the discriminant and the moduli divisor.Comment: 17 pages, the title has been slightly changed, the proofs of Theorem 1.6 and Theorem 3.2 have been simplified and corrected. To appear in "Annales de l'Institut Fourier

Umemura Quadric Fibrations and Maximal Subgroups of Crn(C)Cr_n(\mathbb{C})

We study the equivariant geometry of special quadric fibrations, called Umemura quadric fibrations, as well as the maximality of their automorphism groups inside $Cr_n(\mathbb{C})$. We produce infinite families of pairwise non-conjugate maximal connected algebraic subgroups of $Cr_n(\mathbb{C})$.Comment: 24 pages, comments are welcom

On the B-Semiampleness Conjecture

The B-Semiampleness Conjecture of Prokhorov and Shokurov predicts that the moduli part in a canonical bundle formula is semiample on a birational modification. We prove that the restriction of the moduli part to any sufficiently high divisorial valuation is semiample, assuming the conjecture in lower dimensions.Comment: 26 page