Étude des surfaces algébriques
Étude géométrique sur une question de licence
Even canonical surfaces with small - II
Even sets of nodes on sextic surfaces
We determine the possible even sets of nodes on sextic surfaces in , showing in particular that their cardinalities are exactly the numbers in the set . We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, and of homological and computer algebra on the other. We give a detailed geometric construction for the new case of an even set of 56 nodes, but the ultimate verification of existence...
Éventails et variétés toriques
Every rational surface is separably split.
Everywhere non reduced moduli spaces.
Examples of abelian surfaces in P4.
Examples of liftings of surfaces and a problem in de Rham cohomology
Examples of non-ample normal bundles
Examples of threefolds with Kodaira dimension 1 or 2
Exceptional Bundles On Nodal Enriques Surfaces.
Exceptional linear systems on curves on Del Pezzo surfaces.
Exceptional singular -homology planes
We consider singular -acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is - or -ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type and respectively.
Existence and Degeneration of Kähler-Einstein Metrics on Minimal Algebraic Varieties of General Type.
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....