We explore the birational structure and invariants of a foliated surface ( X , F ) in terms of the adjoint divisor K-F + epsilon K-X, 0 < epsilon & laquo; 1 0 . We then establish a bound on the automorphism group of an adjoint general type foliated surface ...
We give a criterion for a nef divisor D to be semi-ample on a Calabi-Yau threefold X when D3 = 0 = c2 (X)center dot D and c3 (X) 6= 0. As a direct consequence, we show that on such a variety X, if D is strictly nef and.(D) 6= 1, then D is ample; we also sh ...
We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index 1 covers for n-dimensional klt singularities. We give an application to the study of lo ...
We prove that rationally connected Calabi-Yau 3-folds with Kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected 3 folds of epsilon-CY type form a birationally bounded family for epsilon > 0. ...
We consider the problem of determining which Fano manifolds can be realised as fibres of a Mori fibre space. In particular, we study the case of toric varieties, Fano manifolds with high index and some Fano manifolds with high Picard rank. ...
We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi-Yau manifolds Y -> X with a rational section, provided that dim(Y)
