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Existence of minimal models for varieties of log general type
Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.
ACC for log canonical thresholds
We show that log canonical thresholds satisfy the ACC.
Rational curves on quasi-projective surfaces
Introduction and statement of results Glossary of notation and conventions Gorenstein del Pezzo surfaces Bug-eyed covers Log deformation theory Criteria for log uniruledness Reduction toExpand
Boundedness of pluricanonical maps of varieties of general type
Using the techniques of [20] and [10], we prove that certain log forms may be lifted from a divisor to the ambient variety. As a consequence of this result, following [22], we show that: For anyExpand
On Shokurov's rational connectedness conjecture
We prove a conjecture of V. V. Shokurov which in particular implies that the fibers of a resolution of a variety with divisorial log terminal singularities are rationally chain connected.
ON THE BIRATIONAL AUTOMORPHISMS OF VARIETIES OF GENERAL TYPE
We show that the number of birational automorphisms of a variety of general type X is bounded by c vol(X;KX), where c is a constant that only depends on the dimension of X.
The Sarkisov program
Any two birational Mori fibre spaces are connected by a sequence of Sarkisov links.
Threefold thresholds
Abstract.We prove that the set of accumulation points of thresholds in dimension three is equal to the set of thresholds in dimension two, excluding one.
Boundedness of log terminal Fano pairs of bounded index
We prove a conjecture of Batryev which states that the family of all Fano varieties with kawamata log terminal singularities and fixed index, forms a bounded family.
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