Algorithmetical aspects of the problem of classifying multi-projections of veronesian varieties.
Amibes de variétés algébriques et dénombrement de courbes
Les amibesdes variétés algébriques dans sont les images de ces variétés par l’application des moments , . Des résultats obtenus par G. Mikhalkin montrent l’utilité des amibes pour l’étude des variétés algébriques réelles et complexes. Les amibes peuvent être déformées en des complexes polyédraux appelésvariétés algébriques tropicales. Cette déformation permet, en particulier, de calculer les invariants de Gromov-Witten du plan projectif et d’autres surfaces toriques en dénombrant des courbes...
Ample divisors on the blow up of P3 at points.
Ample line bundles on smooth surfaces.
An affirmative answer to a question of Ciliberto.
An effective Bertini theorem over finite fields.
An example of two homeomorphic, nondiffeomorphic complete intersection surfaces.
An extremal property of Rokhlin' s inequality for real algebraic curves.
An introduction to quantum sheaf cohomology
In this note we review “quantum sheaf cohomology,” a deformation of sheaf cohomology that arises in a fashion closely akin to (and sometimes generalizing) ordinary quantum cohomology. Quantum sheaf cohomology arises in the study of (0,2) mirror symmetry, which we review. We then review standard topological field theories and the A/2, B/2 models, in which quantum sheaf cohomology arises, and outline basic definitions and computations. We then discuss (2,2) and (0,2) supersymmetric Landau-Ginzburg...
Analytic subsets of products of infinite-dimensional projective spaces.
Apollonius' contact problem in -space in view of enumerative geometry.
Application de la généralisation du principe de correspondance à la théorie de l'élimination
Applications of iterated curve blow-up to set theoretic complete intersections in ...3.
Arithmetically normal sheaves
Arrangements d'hyperplans et sommes de Gauss
Arrangements of lines and monodromy of plane curves
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.