Existence of Rank 3 Vector Bundles with Given Chern Classes on Homogeneous Rational 3-Folds.
Existence of rational points on smooth projective varieties
Explicit birational geometry of threefolds of general type, I
Let be a complex nonsingular projective 3-fold of general type. We prove and for some positive integer . A direct consequence is the birationality of the pluricanonical map for all . Besides, the canonical volume has a universal lower bound .
Explicit reduction theory for Siegel modular threefolds.
Explicit resolutions of double point singularities of surfaces.
Locally analytically, any isolated double point occurs as a double cover of a smooth surface. It can be desingularized explicitly via the canonical resolution, as it is very well-known. In this paper we explicitly compute the fundamental cycle of both the canonical and minimal resolution of a double point singularity and we classify those for which the fundamental cycle differs from the fiber cycle. Moreover we compute the conditions that a double point singularity imposes to pluricanonical systems....
Extending extremal contractions from an ample section.
Extension of maps defined on many fibres.
Let S be a fibred surface. We prove that the existence of morphisms from non countably many fibres to curves implies, up to base change, the existence of a rational map from S to another surface fibred over the same base reflecting the properties of the original morphisms. Under some conditions of unicity base change is not needed and one recovers exactly the initial maps.
Extensions of vector bundles and rationality of certain moduli spaces of stable bundles.
Extremal contractions from 4-dimensional manifolds to 3-folds
Extremal rational elliptic surfaces in characteristic p. I. Beauville surfaces.
Extremal rays on higher dimensional projective varieties.
Extremal rays on smooth threefolds