The canonical filtration of higher dimensional purely elliptic singularity of a special type.
The Hilbert Modular Surface of a Real Quadratic Field.
The Mukai conjecture for log Fano manifolds
For a log Fano manifold (X,D) with D ≠ 0 and of the log Fano pseudoindex ≥2, we prove that the restriction homomorphism Pic(X) → Pic(D 1) of Picard groups is injective for any irreducible component D 1 ⊂ D. The strategy of our proof is to run a certain minimal model program and is similar to Casagrande’s argument. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture).
The number of conjugacy classes of elements of the Cremona group of some given finite order
This note presents the study of the conjugacy classes of elements of some given finite order in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if is even, or , and that it is equal to (respectively ) if (respectively if ) and to for all remaining odd orders. Some precise representative elements of the classes are given.
The Number of the Minimal Models for a 3- Fold of General Type is Finite.
The scheme of connected components of the Néron model of an algebraic torus.
Three-dimensional terminal toric flips
We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.
Threefolds with nef anticanonical bundles.
In this paper we study the global structure of projective threefolds X whose anticanonical bundle -KX is nef.
Towards a Mori theory on compact Kähler threefolds III
Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e. is nef) is good,i.e.its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of is generated by global sections); unless is simple. “Simple“ means that there is no compact subvariety through the very general point of and not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical...
Towards the classification of weak Fano threefolds with ρ = 2
In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases...
Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations
Let be a normal projective variety, and let be an ample Cartier divisor on . Suppose that is not the projective space. We prove that the twisted cotangent sheaf is generically nef with respect to the polarisation . As an application we prove a Kobayashi-Ochiai theorem for foliations: if is a foliation such that , then is at most the rank of .
Two theorems on elementary contractions.