Analytic Cycles and Vector Bundles on Non-Compact Algebraic Varieties.
Analytic deviation of ideals and intersection theory of analytic spaces.
Annulation du H1 et systèmes paracanoniques sur les surfaces.
Anticanonical Models of Rational Surfaces.
Appendice: «La classe fondamentale relative d'un cycle»
Appendix : “Picard groups of Zariski surfaces”
Appendix to "Plücker conditions on plane rational curves": Families of rational plane curves.
Applications of the Ein-Lazarsfeld cirterion for spannedness of adjoint bundles.
Applications of the Kähler-Einstein-Calabi-Yau Metric to Moduli of K3 Surfaces.
Applications of weight-two motivic cohomology.
Arakelov Chow groups of abelian schemes, arithmetic Fourier transform, and analogues of the standard conjectures of Lefschetz type.
Arithmetic discriminants and horizontal intersections.
Arithmetic intersection theory
Arithmetic of 0-cycles on varieties defined over number fields
Let be a rationally connected algebraic variety, defined over a number field We find a relation between the arithmetic of rational points on and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for -rational points on for all finite extensions (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles of degree...
Arithmetical graphs.
Arithmetically Gorenstein curves on arithmetically Cohen-Macaulay surfaces.
Let Sigma C PN be a smooth connected arithmetically Cohen-Macaulay surface. Then there are at most finitely many complete linear systems on Sigma, not of the type |kH - K| (H hyperplane section and K canonical divisor on Sigma), containing arithmetically Gorenstein curves.
Around rationality of cycles
We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.
Around the Gysin triangle. II.
Associate forms, joins, multiplicities and an intrinsic elimination theory
Asymptotic behaviour of numerical invariants of algebraic varieties
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.