Babbage's Conjecture, Contact of Surfaces, Symmetric Determinantal Varieties and Applications.
Base curves of multicanonical systems on threefolds
Birational invariants of algebraic varieties.
Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.
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 for the number of moduli for irregular varieties of general type.
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 general fibre is a rational curve. If is the Cartier index of the fibre, it was expected that would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in , we provide a bound and an example where the smallest integer that clears the denominators of the moduli part is . Moreover we prove that even locally the denominators depend...