105 research outputs found
Around and beyond the canonical class
This survey is an invitation to recent developments in higher dimensional
birational geometry.Comment: to appear in "Birational geometry, rational curves, and arithmetic,
Simons Symposium Proceedings", Springer Verla
On the Cone conjecture for Calabi-Yau manifolds with Picard number two
Following a recent work of Oguiso, we calculate explicitly the groups of
automorphisms and birational automorphisms on a Calabi-Yau manifold with Picard
number two. When the group of birational automorphisms is infinite, we prove
that the Cone conjecture of Morrison and Kawamata holds.Comment: to appear in Math. Res. Let
On the existence of minimal models for log canonical pairs
We show that minimal models of log canonical pairs exist, assuming the
existence of minimal models of smooth varieties.Comment: v3: minor changes; title changed; to appear in Publ. Res. Inst. Math.
Sc
The Minimal Model Program Revisited
We give a light introduction to some recent developments in Mori theory, and
to our recent direct proof of the finite generation of the canonical ring.Comment: to appear in Contributions to Algebraic Geometry, EMS Series of
Congress Report
Abundance for varieties with many differential forms
We prove that the abundance conjecture holds on a variety with mild
singularities if has many reflexive differential forms with coefficients in
pluricanonical bundles, assuming the Minimal Model Program in lower dimensions.
This implies, for instance, that under this condition, hermitian semipositive
canonical divisors are almost always semiample, and that klt pairs whose
underlying variety is uniruled have good models in many circumstances. When the
numerical dimension of is , our results hold unconditionally in every
dimension. We also treat a related problem on the semiampleness of nef line
bundles on Calabi-Yau varieties
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