Existence of minimal models for varieties of log general type
- C. Hacon, J. McKernan
- Mathematics
- 5 October 2006
Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.
ACC for log canonical thresholds
- C. Hacon, J. McKernan, Chenyang Xu
- Physics, MathematicsAnnals of Mathematics
- 21 August 2012
We show that log canonical thresholds satisfy the ACC.
Rational curves on quasi-projective surfaces
- S. Keel, J. McKernan
- Mathematics
- 25 July 1997
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 to…
Boundedness of pluricanonical maps of varieties of general type
- C. Hacon, J. McKernan
- Mathematics
- 15 April 2005
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 any…
On Shokurov's rational connectedness conjecture
- C. Hacon, J. McKernan
- Mathematics
- 15 April 2005
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
- C. Hacon, J. McKernan, Chenyang Xu
- MathematicsAnnals of Mathematics
- 5 November 2010
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.
Log abundance theorem for threefolds
- S. Keel, K. Matsuki, J. McKernan
- Mathematics
- 1 July 1994
The Augmented Base Locus in Positive Characteristic
- P. Cascini, J. McKernan, M. Mustaţă
- MathematicsProceedings of the Edinburgh Mathematical Society
- 14 November 2011
Abstract Let L be a nef line bundle on a projective scheme X in positive characteristic. We prove that the augmented base locus of L is equal to the union of the irreducible closed subsets V of X…
Boundedness of moduli of varieties of general type
- C. Hacon, J. McKernan, Chenyang Xu
- Mathematics
- 3 December 2014
We show that the family of semi log canonical pairs with ample log canonical class and with fixed volume is bounded.
The Sarkisov program
- C. Hacon, J. McKernan
- Mathematics
- 7 May 2009
Any two birational Mori fibre spaces are connected by a sequence of Sarkisov links.
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